{"id":1365,"date":"2020-07-31T20:34:32","date_gmt":"2020-08-01T00:34:32","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/use-a-problem-solving-strategy\/"},"modified":"2021-03-24T10:57:05","modified_gmt":"2021-03-24T14:57:05","slug":"use-a-problem-solving-strategy","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/use-a-problem-solving-strategy\/","title":{"raw":"5.7 Use a Problem-Solving Strategy","rendered":"5.7 Use a Problem-Solving Strategy"},"content":{"raw":"[latexpage]\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nBy the end of this section, you will be able to:\n<ul>\n \t<li>Approach word problems with a positive attitude<\/li>\n \t<li>Use a problem-solving strategy for word problems<\/li>\n \t<li>Solve number problems<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Approach Word Problems with a Positive Attitude<\/h1>\n<p id=\"fs-id1168344306748\">\u201cIf you think you can\u2026 or think you can\u2019t\u2026 you\u2019re right.\u201d\u2014Henry Ford<\/p>\n<p id=\"fs-id1168344156191\">The world is full of word problems! Will my income qualify me to rent that apartment? How much punch do I need to make for the party? What size diamond can I afford to buy my girlfriend? Should I fly or drive to my family reunion?<\/p>\n<p id=\"fs-id1168344196663\">How much money do I need to fill the car with gas? How much tip should I leave at a restaurant? How many socks should I pack for vacation? What size turkey do I need to buy for Thanksgiving dinner, and then what time do I need to put it in the oven? If my sister and I buy our mother a present, how much does each of us pay?<\/p>\n<p id=\"fs-id1168344337114\">Now that we can solve equations, we are ready to apply our new skills to word problems. Do you know anyone who has had negative experiences in the past with word problems? Have you ever had thoughts like the student below?<\/p>\n\n<div id=\"CNX_ElemAlg_Figure_03_01_002\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">Negative thoughts can be barriers to success.<\/div>\n\n[caption id=\"\" align=\"aligncenter\" width=\"627\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/07\/CNX_ElemAlg_Figure_03_01_002_img_new.jpg\" alt=\"A student is shown with thought bubbles saying \u201cI don\u2019t know whether to add, subtract, multiply, or divide!,\u201d \u201cI don\u2019t understand word problems!,\u201d \u201cMy teachers never explained this!,\u201d \u201cIf I just skip all the word problems, I can probably still pass the class,\u201d and \u201cI just can\u2019t do this!\u201d\" width=\"627\" height=\"422\" data-media-type=\"image\/jpeg\"> Figure .1[\/caption]\n\n<\/div>\n<p id=\"fs-id1168344164823\">When we feel we have no control, and continue repeating negative thoughts, we set up barriers to success. We need to calm our fears and change our negative feelings.<\/p>\n<p id=\"fs-id1168344117014\">Start with a fresh slate and begin to think positive thoughts. If we take control and believe we can be successful, we will be able to master word problems! Read the positive thoughts in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_03_01_003\">(Figure 2)<\/a> and say them out loud.<\/p>\n\n<div id=\"CNX_ElemAlg_Figure_03_01_003\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">Thinking positive thoughts is a first step towards success.<\/div>\n\n[caption id=\"\" align=\"aligncenter\" width=\"593\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_003.jpg\" alt=\"A student is shown with thought bubbles saying \u201cWhile word problems were hard in the past, I think I can try them now,\u201d \u201cI am better prepared now. I think I will begin to understand word problems,\u201d \u201cI think I can! I think I can!,\u201d and \u201cIt may take time, but I can begin to solve word problems.\u201d\" width=\"593\" height=\"426\" data-media-type=\"image\/jpeg\"> Figure .2[\/caption]\n\n<\/div>\n<p id=\"fs-id1168344198246\">Think of something, outside of school, that you can do now but couldn\u2019t do 3 years ago. Is it driving a car? Snowboarding? Cooking a gourmet meal? Speaking a new language? Your past experiences with word problems happened when you were younger\u2014now you\u2019re older and ready to succeed!<\/p>\n\n<h1 data-type=\"title\">Use a Problem-Solving Strategy for Word Problems<\/h1>\n<p id=\"fs-id1168344342341\">We have reviewed translating English phrases into algebraic expressions, using some basic mathematical vocabulary and symbols. We have also translated English sentences into algebraic equations and solved some word problems. The word problems applied math to everyday situations. We restated the situation in one sentence, assigned a variable, and then wrote an equation to solve the problem. This method works as long as the situation is familiar and the math is not too complicated.<\/p>\n<p id=\"fs-id1168344254595\">Now, we\u2019ll expand our strategy so we can use it to successfully solve any word problem. We\u2019ll list the strategy here, and then we\u2019ll use it to solve some problems. We summarize below an effective strategy for problem solving.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Use a Problem-Solving Strategy to Solve Word Problems.<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1166424800382\" class=\"stepwise\" type=\"1\">\n \t<li><strong data-effect=\"bold\">Read<\/strong> the problem. Make sure all the words and ideas are understood.<\/li>\n \t<li><strong data-effect=\"bold\">Identify<\/strong> what we are looking for.<\/li>\n \t<li><strong data-effect=\"bold\">Name<\/strong> what we are looking for. Choose a variable to represent that quantity.<\/li>\n \t<li><strong data-effect=\"bold\">Translate<\/strong> into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebraic equation.<\/li>\n \t<li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li>\n \t<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\n \t<li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344229115\" class=\"howto\" data-type=\"note\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344286696\" data-type=\"problem\">\n<p id=\"fs-id1168344191428\">Pilar bought a purse on sale for \\$18, which is one-half of the original price. What was the original price of the purse?<\/p>\n\n<\/div>\n<div id=\"fs-id1168344117081\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168344074298\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem. Read the problem two or more times if necessary. Look up any unfamiliar words in a dictionary or on the internet.<\/p>\n\n<ul id=\"fs-id1166424861466\" data-bullet-style=\"bullet\">\n \t<li><em data-effect=\"italics\">In this problem, is it clear what is being discussed? Is every word familiar?<\/em><\/li>\n<\/ul>\n<p id=\"fs-id1168344164753\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for. Did you ever go into your bedroom to get something and then forget what you were looking for? It\u2019s hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!<\/p>\n\n<ul id=\"fs-id1166424917531\" data-bullet-style=\"bullet\">\n \t<li><em data-effect=\"italics\">In this problem, the words \u201cwhat was the original price of the purse\u201d tell us what we need to find.<\/em><\/li>\n<\/ul>\n<p id=\"fs-id1168344318843\"><strong data-effect=\"bold\">Step 3. Name<\/strong> what we are looking for. Choose a variable to represent that quantity. We can use any letter for the variable, but choose one that makes it easy to remember what it represents.<\/p>\n\n<ul id=\"fs-id1166424772657\" data-bullet-style=\"bullet\">\n \t<li>Let \\(p=\\) the original price of the purse.<\/li>\n<\/ul>\n<p id=\"fs-id1168344229632\"><strong data-effect=\"bold\">Step 4. Translate<\/strong> into an equation. It may be helpful to restate the problem in one sentence with all the important information. Translate the English sentence into an algebraic equation.<\/p>\n<p id=\"fs-id1168344298465\">Reread the problem carefully to see how the given information is related. Often, there is one sentence that gives this information, or it may help to write one sentence with all the important information. Look for clue words to help translate the sentence into algebra. Translate the sentence into an equation.<\/p>\n\n<table id=\"eip-id1167269958572\" style=\"width: 100%;\" summary=\"We are given the direction to restate the problem in one sentence with all the important information. To the right of this, we have 18 is one-half the original price. Below this, we are told to translate this into an equation. Hence we have 18 equals 1\/2 times p.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Restate the problem in one sentence with all the important information.<\/td>\n<td><span id=\"eip-id1167265664116\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_004a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Translate into an equation.<\/td>\n<td><span id=\"eip-id1167265757342\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_004b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344281297\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation using good algebraic techniques. Even if you know the solution right away, using good algebraic techniques here will better prepare you to solve problems that do not have obvious answers.<\/p>\n\n<table id=\"eip-id1167269971537\" style=\"width: 100%;\" summary=\"We are given the direction to restate the problem in one sentence with all the important information. To the right of this, we have 18 is one-half the original price. Below this, we are told to translate this into an equation. Hence we have 18 equals 1\/2 times p.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Solve the equation.<\/td>\n<td><span id=\"eip-id1167270176483\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_005a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by 2.<\/td>\n<td><span id=\"eip-id1167265367934\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_005b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1167266374820\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_005c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344155673\"><strong data-effect=\"bold\">Step 6. Check<\/strong> the answer in the problem to make sure it makes sense. We solved the equation and found that \\(p=36\\), which means \u201cthe original price\u201d was \\$36<\/p>\n\n<ul id=\"fs-id1166424777751\" data-bullet-style=\"bullet\">\n \t<li><em data-effect=\"italics\">Does \\$36 make sense in the problem? Yes, because 18 is one-half of 36, and the purse was on sale at half the original price.<\/em><\/li>\n<\/ul>\n<p id=\"fs-id1168344087441\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question with a complete sentence. The problem asked \u201cWhat was the original price of the purse?\u201d<\/p>\n\n<ul id=\"fs-id1166424844683\" data-bullet-style=\"bullet\">\n \t<li><em data-effect=\"italics\">The answer to the question is: \u201cThe original price of the purse was \\$36.\u201d<\/em><\/li>\n<\/ul>\n<p id=\"fs-id1168344247891\">If this were a homework exercise, our work might look like this:<\/p>\n<p id=\"fs-id1168344192192\">Pilar bought a purse on sale for \\$18, which is one-half the original price. What was the original price of the purse?<\/p>\n\n<table id=\"eip-id1167270180122\" style=\"width: 100%;\" summary=\"We are told to let p equal the original price. Below this, we are told 18 is one-half the original price. To the right of this, we have 18 equals 1\/2 times p. Below this, we are told to check whether \ud83d\udcb236 is a reasonable price for a purse? The answer is yes. To the right of this, we have 2 times 18 equals 2 times 1\/2 times p. Then below this, we have 36 equals p. Below this, we are asked if 18 is one-half of 36. We have 18 equals with a question mark over it 1\/2 times 36. Below this, we have 18 equals 18.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 291px;\"><\/td>\n<td style=\"width: 264px;\">Let \\(p=\\) the original price.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 291px;\"><\/td>\n<td style=\"width: 264px;\">18 is one-half the original price.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 291px;\"><\/td>\n<td style=\"width: 264px;\"><span id=\"eip-id1167269978911\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_006a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 291px;\">Multiply both sides by 2.<\/td>\n<td style=\"width: 264px;\"><span id=\"eip-id1167261007231\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_006b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 291px;\">Simplify.<\/td>\n<td style=\"width: 264px;\"><span id=\"eip-id1167266207221\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_006c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 291px;\">Check. Is \\$36 a reasonable price for a purse?<\/td>\n<td style=\"width: 264px;\">Yes.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 291px;\">Is 18 one half of 36?<\/td>\n<td style=\"width: 264px;\">\\(18\\stackrel{?}{=}\\frac{1}{2}\\cdot 36\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 291px;\"><\/td>\n<td style=\"width: 264px;\">\\(18=18\\)\u2713<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 291px;\"><\/td>\n<td style=\"width: 264px;\">The original price of the purse was \\$36.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344295590\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344119591\" data-type=\"exercise\">\n<div id=\"fs-id1168344188976\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344188976\" data-type=\"problem\">\n<p id=\"fs-id1168344208579\">Joaquin bought a bookcase on sale for \\$120, which was two-thirds of the original price. What was the original price of the bookcase?<\/p>\n\n<\/div>\n<div id=\"fs-id1168344227446\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344087983\">\\$180<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344247292\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344330742\" data-type=\"exercise\">\n<div id=\"fs-id1168344313530\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344313530\" data-type=\"problem\">\n<p id=\"fs-id1168344341142\">Two-fifths of the songs in Mariel\u2019s playlist are country. If there are 16 country songs, what is the total number of songs in the playlist?<\/p>\n\n<\/div>\n<div id=\"fs-id1168344076283\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344334775\">40<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344249163\">Let\u2019s try this approach with another example.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344164632\" data-type=\"problem\">\n<p id=\"fs-id1168344188180\">Ginny and her classmates formed a study group. The number of girls in the study group was three more than twice the number of boys. There were 11 girls in the study group. How many boys were in the study group?<\/p>\n\n<\/div>\n<div id=\"fs-id1168344081872\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1167264182522\" style=\"height: 228px; width: 100%;\" summary=\"We are given a table with instructions on the left and mathematical statements on the right. It starts with Step 1. Read the problem. Then we have Step 2. Identify what we are looking for. To the right of this, we have \u201cHow many boys did he bring?\u201d Then we have Step 3. Name. Choose a variable to represent the number of boys. To the right of this, we let b equal the number of boys. Then we have Step 4. Translate. Restate the problem in one sentence with all the important information. To the right of this, we have The number of girls (11) was three more than twice the number of boys. Then, translate this into an equation, which gives 11 equals 2b plus 3. Then we have Step 5. Solve the equation. To the right of this, we have 11 equals 2b plus 3. We are told to subtract 3 from each side, so we have 11 minus 3 equals 2b plus 3 minus 3. We are told to simplify, which gives us 8 equals 2b. Then we are told to divide each side by 2, which gives 8\/2 equals 2b\/2. We are told to simplify, which gives 4 equals b. Then we have Step 6. Check. First, is our answer reasonable? Yes, having 4 boys in a study group seems OK. The problem says the number of girls was three more than twice the number of boys. If there are four boys, does that make eleven girls? Twice 4 boys is 8. Three more than 8 is 11. Finally, we have Step 7. Answer the question: \u201cThere were 4 boys in the study group.\u201d\" data-label=\"\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 337.406px;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"height: 14px; width: 315.406px;\"><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 337.406px;\"><strong>Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td style=\"height: 30px; width: 315.406px;\">How many boys were in the study group?<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 337.406px;\"><strong>Step 3. Name.<\/strong> Choose a variable to represent the number of boys.<\/td>\n<td style=\"height: 14px; width: 315.406px;\">Let \\(n=\\) the number of boys.<\/td>\n<\/tr>\n<tr style=\"height: 33px;\">\n<td style=\"height: 33px; width: 337.406px;\"><strong>Step 4. Translate.<\/strong> Restate the problem in one sentence with all the important information.<\/td>\n<td style=\"height: 33px; width: 315.406px;\"><span id=\"eip-id1167265328711\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 337.406px;\">Translate into an equation.<\/td>\n<td style=\"height: 14px; width: 315.406px;\"><span id=\"eip-id1167270022563\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_007b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 337.406px;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"height: 14px; width: 315.406px;\"><span id=\"eip-id1167269991276\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_007c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 337.406px;\">Subtract 3 from each side.<\/td>\n<td style=\"height: 14px; width: 315.406px;\"><span id=\"eip-id1167261207104\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_007d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 337.406px;\">Simplify.<\/td>\n<td style=\"height: 14px; width: 315.406px;\"><span id=\"eip-id1167261195902\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_007e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 337.406px;\">Divide each side by 2.<\/td>\n<td style=\"height: 23px; width: 315.406px;\"><span id=\"eip-id1167270244307\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_007f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 337.406px;\">Simplify.<\/td>\n<td style=\"height: 14px; width: 315.406px;\"><span id=\"eip-id1167269996886\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_007g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 337.406px;\"><strong>Step 6. Check.<\/strong> First, is our answer reasonable?<\/td>\n<td style=\"height: 30px; width: 315.406px;\">Yes, having 4 boys in a study group seems OK. The problem says the number of girls was 3 more than twice the number of boys. If there are four boys, does that make eleven girls? Twice 4 boys is 8. Three more than 8 is 11.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 337.406px;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"height: 14px; width: 315.406px;\">There were 4 boys in the study group.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344318972\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344162058\" data-type=\"exercise\">\n<div id=\"fs-id1168344285800\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344285800\" data-type=\"problem\">\n<p id=\"fs-id1168344083134\">Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was 3 more than twice the number of notebooks. He bought 7 textbooks. How many notebooks did he buy?<\/p>\n\n<\/div>\n<div id=\"fs-id1168344226688\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344207955\">2<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344248666\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344252987\" data-type=\"exercise\">\n<div id=\"fs-id1168344281885\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344281885\" data-type=\"problem\">\n<p id=\"fs-id1168344228250\">Gerry worked Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is eight more than twice the number of crossword puzzles. He completed 22 Sudoku puzzles. How many crossword puzzles did he do?<\/p>\n\n<\/div>\n<div id=\"fs-id1168344242946\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344125519\">7<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Solve Number Problems<\/h1>\n<p id=\"fs-id1168344126170\">Now that we have a problem solving strategy, we will use it on several different types of word problems. The first type we will work on is \u201cnumber problems.\u201d Number problems give some clues about one or more numbers. We use these clues to write an equation. Number problems don\u2019t usually arise on an everyday basis, but they provide a good introduction to practicing the problem solving strategy outlined above.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344213738\" data-type=\"problem\">\n<p id=\"fs-id1168344120473\">The difference of a number and six is 13. Find the number.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344198836\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1167271015539\" style=\"width: 100%;\" summary=\"We are given a table with instructions on the left and mathematical statements on the right. It starts with Step 1. Read the problem. Are all the words familiar? Then we have Step 2. Identify what we are looking for. To the right of this, we have \u201cthe number.\u201d Then we have Step 3. Name. Choose a variable to represent the number. To the right of this, we let n equal the number. Then we have Step 4. Translate. Remember to look for clue words like \u201cdifference\u2026 of\u2026 and.\u201d Restate the problem as one sentence. To the right of this, we have The difference of the number and 6 is 13. Then, translate this into an equation, which gives n minus 6 equals 13. Then we have Step 5. Solve the equation. To the right of this, we have n minus 6 equals 13. We are told to simplify, which gives us n equals 19. Then we have Step 6. Check. The difference of 19 and 6 is 13. It checks! Finally, we have Step 7. Answer the question: \u201cThe number is 19.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><strong>Step 1. Read<\/strong> the problem. Are all the words familiar?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td>the number<\/td>\n<\/tr>\n<tr>\n<td><strong>Step 3. Name.<\/strong> Choose a variable to represent the number.<\/td>\n<td>Let \\(n=\\) the number.<\/td>\n<\/tr>\n<tr>\n<td><strong>Step 4. Translate.<\/strong> Remember to look for clue words like \"difference... of... and...\"<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Restate the problem as one sentence.<\/td>\n<td><span id=\"eip-id1167267549086\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Translate into an equation.<\/td>\n<td><span id=\"eip-id1167267573042\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1167271354701\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_008c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"fs-id1169149211312\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_008d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><strong>Step 6. Check.<\/strong><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The difference of 19 and 6 is 13. It checks!<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td>The number is 19.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344196679\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344208705\" data-type=\"exercise\">\n<div id=\"fs-id1168344198937\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344198937\" data-type=\"problem\">\n<p id=\"fs-id1168344115069\">The difference of a number and eight is 17. Find the number.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344102861\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344293018\">25<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344318146\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344306281\" data-type=\"exercise\">\n<div id=\"fs-id1168344306283\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344306283\" data-type=\"problem\">\n<p id=\"fs-id1168344332115\">The difference of a number and eleven is \\(-7\\). Find the number.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344287715\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344342077\">4<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344254046\" data-type=\"problem\">\n<p id=\"fs-id1168344246247\">The sum of twice a number and seven is 15. Find the number.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344208213\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1167268159009\" style=\"width: 100%;\" summary=\"We are given a table with instructions on the left and mathematical statements on the right. It starts with Step 1. Read the problem. Are all the words familiar? Then we have Step 2. Identify what we are looking for. To the right of this, we have \u201cthe number.\u201d Then we have Step 3. Name. Choose a variable to represent the number. To the right of this, we let n equal the number. Then we have Step 4. Translate. Remember to look for clue words like \u201cdifference\u2026 of\u2026 and.\u201d Restate the problem as one sentence. To the right of this, we have The difference of the number and 6 is 13. Then, translate this into an equation, which gives n minus 6 equals 13. Then we have Step 5. Solve the equation. To the right of this, we have n minus 6 equals 13. We are told to simplify, which gives us n equals 19. Then we have Step 6. Check. The difference of 19 and 6 is 13. It checks! Finally, we have Step 7. Answer the question: \u201cThe number is 19.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 366.406px;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"width: 286.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\"><strong>Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td style=\"width: 286.406px;\">the number<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\"><strong>Step 3. Name.<\/strong> Choose a variable to represent the number.<\/td>\n<td style=\"width: 286.406px;\">Let \\(n=\\) the number.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\"><strong>Step 4. Translate.<\/strong><\/td>\n<td style=\"width: 286.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\">Restate the problem as one sentence.<\/td>\n<td style=\"width: 286.406px;\"><span id=\"eip-id1167266669989\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_009a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\">Translate into an equation.<\/td>\n<td style=\"width: 286.406px;\"><span id=\"eip-id1167271268957\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_009b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"width: 286.406px;\"><span id=\"eip-id1167271268973\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_009c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\">Subtract 7 from each side and simplify.<\/td>\n<td style=\"width: 286.406px;\"><span id=\"eip-id1167267708487\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_009d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\">Divide each side by 2 and simplify.<\/td>\n<td style=\"width: 286.406px;\"><span id=\"eip-id1167267708501\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_009e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\"><strong>Step 6. Check.<\/strong><\/td>\n<td style=\"width: 286.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\">Is the sum of twice 4 and 7 equal to 15?<\/td>\n<td style=\"width: 286.406px;\">\\(\\begin{array}{ccc}\\hfill 2\\cdot 4+7&amp; \\stackrel{?}{=}\\hfill &amp; 15\\hfill \\\\ \\hfill 15&amp; =\\hfill &amp; 15\\checkmark\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"width: 286.406px;\">The number is 4.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344167538\">Did you notice that we left out some of the steps as we solved this equation? If you\u2019re not yet ready to leave out these steps, write down as many as you need.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344300575\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344294400\" data-type=\"exercise\">\n<div id=\"fs-id1168344294402\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344294402\" data-type=\"problem\">\n<p id=\"fs-id1168344164747\">The sum of four times a number and two is 14. Find the number.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344227099\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344227102\">3<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344248658\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344294861\" data-type=\"exercise\">\n<div id=\"fs-id1168344294864\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344294864\" data-type=\"problem\">\n<p id=\"fs-id1168344249726\">The sum of three times a number and seven is 25. Find the number.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344246276\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344246278\">6<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344249797\">Some number word problems ask us to find two or more numbers. It may be tempting to name them all with different variables, but so far we have only solved equations with one variable. In order to avoid using more than one variable, we will define the numbers in terms of the same variable. Be sure to read the problem carefully to discover how all the numbers relate to each other.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344156561\" data-type=\"problem\">\n<p id=\"fs-id1168344248092\">One number is five more than another. The sum of the numbers is 21. Find the numbers.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344317629\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 50%;\"><strong>Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td style=\"height: 30px; width: 50%;\">We are looking for two numbers.<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 50%;\"><strong>Step 3. Name.<\/strong> We have two numbers to name and need a name for each.<\/td>\n<td style=\"height: 30px; width: 50%;\"><\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"height: 46px; width: 50%;\">Choose a variable to represent the first number.<\/td>\n<td style=\"height: 46px; width: 50%;\">Let \\(n={1}^{\\mathrm{st}}\\) number.<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 50%;\">What do we know about the second number?<\/td>\n<td style=\"height: 30px; width: 50%;\">One number is five more than another.<\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"height: 46px; width: 50%;\"><\/td>\n<td style=\"height: 46px; width: 50%;\">\\(n+5={2}^{\\mathrm{nd}}\\) number<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 50%;\"><strong>Step 4. Translate. <\/strong>Restate the problem as one sentence with all the important information.<\/td>\n<td style=\"height: 30px; width: 50%;\">The sum of the 1<sup>st<\/sup> number and the 2<sup>nd<\/sup> number is 21.<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px; width: 50%;\">Translate into an equation.<\/td>\n<td style=\"height: 16px; width: 50%;\"><span id=\"eip-id1167270290107\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\">Substitute the variable expressions.<\/td>\n<td style=\"height: 14px; width: 50%;\"><span id=\"eip-id1167261276092\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"height: 14px; width: 50%;\"><span id=\"eip-id1167261210912\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\">Combine like terms.<\/td>\n<td style=\"height: 14px; width: 50%;\"><span id=\"eip-id1167265412776\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\">Subtract 5 from both sides and simplify.<\/td>\n<td style=\"height: 14px; width: 50%;\"><span id=\"eip-id1167270270940\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\">Divide by 2 and simplify.<\/td>\n<td style=\"height: 14px; width: 50%;\"><span id=\"eip-id1167269810887\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\">Find the second number, too.<\/td>\n<td style=\"height: 14px; width: 50%;\"><span id=\"eip-id1167265724617\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\"><\/td>\n<td style=\"height: 14px; width: 50%;\"><span id=\"eip-id1167265755574\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\"><\/td>\n<td style=\"height: 14px; width: 50%;\"><span id=\"eip-id1167263283439\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\"><strong>Step 6. Check.<\/strong><\/td>\n<td style=\"height: 14px; width: 50%;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\">Do these numbers check in the problem?<\/td>\n<td style=\"height: 14px; width: 50%;\"><\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"height: 46px; width: 50%;\">Is one number 5 more than the other?<\/td>\n<td style=\"width: 50%; height: 46px;\">\\(\\phantom{\\rule{1.6em}{0ex}}13\\stackrel{?}{=}8+5\\)<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 50%;\">Is thirteen 5 more than 8? Yes.<\/td>\n<td style=\"width: 50%; height: 30px;\">\\(\\phantom{\\rule{1.6em}{0ex}}13=13\\)\u2713<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\">Is the sum of the two numbers 21?<\/td>\n<td style=\"width: 50%; height: 14px;\">\\(8+13\\stackrel{?}{=}21\\)<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 50%;\"><\/td>\n<td style=\"width: 50%; height: 30px;\">\\(\\phantom{\\rule{1.6em}{0ex}}21=21\\)\u2713<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 16px; width: 50%;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"height: 16px; width: 50%;\">The numbers are 8 and 13.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344294396\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344293581\" data-type=\"exercise\">\n<div id=\"fs-id1168344293583\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344293583\" data-type=\"problem\">\n<p id=\"fs-id1168344307620\">One number is six more than another. The sum of the numbers is twenty-four. Find the numbers.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344307624\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344331833\">9, 15<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344124889\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344319163\" data-type=\"exercise\">\n<div id=\"fs-id1168344319165\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344319165\" data-type=\"problem\">\n<p id=\"fs-id1168344319167\">The sum of two numbers is fifty-eight. One number is four more than the other. Find the numbers.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344331562\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344124827\">27, 31<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344307236\" data-type=\"problem\">\n<p id=\"fs-id1168344307238\">The sum of two numbers is negative fourteen. One number is four less than the other. Find the numbers.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344296813\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td style=\"width: 50%;\">We are looking for two numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 3. Name.<\/strong><\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Choose a variable.<\/td>\n<td style=\"width: 50%;\">Let \\(n={1}^{\\mathrm{st}}\\) number.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">One number is 4 less than the other.<\/td>\n<td style=\"width: 50%;\">\\(n-4={2}^{\\mathrm{nd}}\\) number<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 4. Translate. <\/strong><\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Write as one sentence.<\/td>\n<td style=\"width: 50%;\">The sum of the 2 numbers is negative 14.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Translate into an equation.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271084715\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271346165\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Combine like terms.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271102471\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Add 4 to each side and simplify.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271105692\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167268226870\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167267771016\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167267808396\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167268169938\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"fs-id1169149340877\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 6. Check.<\/strong><\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Is \u22129 four less than \u22125?<\/td>\n<td style=\"width: 50%;\">\\(\\phantom{\\rule{1.1em}{0ex}}-5-4\\stackrel{?}{=}-9\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\phantom{\\rule{2.7em}{0ex}}-9=-9\\)\u2713<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Is their sum \u221214?<\/td>\n<td style=\"width: 50%;\">\\(-5+\\left(-9\\right)\\stackrel{?}{=}-14\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\phantom{\\rule{2.3em}{0ex}}-14=-14\\)\u2713<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"width: 50%;\">The numbers are \u22125 and \u22129.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344299552\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344299556\" data-type=\"exercise\">\n<div id=\"fs-id1168344301712\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344301712\" data-type=\"problem\">\n<p id=\"fs-id1168344301714\">The sum of two numbers is negative twenty-three. One number is seven less than the other. Find the numbers.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344282379\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344282382\">\\(-15,-8\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344286120\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344247223\" data-type=\"exercise\">\n<div id=\"fs-id1168344247225\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344247225\" data-type=\"problem\">\n<p id=\"fs-id1168344281911\">The sum of two numbers is \\(-18\\). One number is 40 more than the other. Find the numbers.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344252714\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344228726\">\\(-29,11\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344316446\" data-type=\"problem\">\n<p id=\"fs-id1168344316449\">One number is ten more than twice another. Their sum is one. Find the numbers.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344247697\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\"><strong>Step 2. Identify<\/strong> what you are looking for.<\/td>\n<td style=\"width: 50%; height: 30px;\">We are looking for two numbers.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><strong>Step 3. Name.<\/strong><\/td>\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Choose a variable.<\/td>\n<td style=\"width: 50%; height: 14px;\">Let \\(x={1}^{\\mathrm{st}}\\) number.<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">One number is 10 more than twice another.<\/td>\n<td style=\"width: 50%; height: 30px;\">\\(2x+10={2}^{\\mathrm{nd}}\\) number<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><strong>Step 4. Translate. <\/strong><\/td>\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Restate as one sentence.<\/td>\n<td style=\"width: 50%; height: 14px;\">Their sum is one.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<td style=\"width: 50%; height: 14px;\">The sum of the two numbers is 1.<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">Translate into an equation.<\/td>\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1167261277458\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_012a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">Combine like terms.<\/td>\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1167263282944\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_012b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">Subtract 10 from each side.<\/td>\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1167263494986\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_012c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">Divide each side by 3.<\/td>\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1167270181053\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_012d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\"><\/td>\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1167265669857\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_012e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\"><\/td>\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1167269925286\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_012f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 50%; height: 18px;\"><\/td>\n<td style=\"width: 50%; height: 18px;\"><span id=\"eip-id1167270172734\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_012g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\"><\/td>\n<td style=\"width: 50%; height: 15px;\"><span id=\"fs-id1169148888999\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_012h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><strong>Step 6. Check.<\/strong><\/td>\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">Is ten more than twice \u22123 equal to 4?<\/td>\n<td style=\"width: 50%;\">\\(2\\left(-3\\right)+10\\stackrel{?}{=}4\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<td style=\"width: 50%;\">\\(\\phantom{\\rule{1em}{0ex}}-6+10\\stackrel{?}{=}4\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<td style=\"width: 50%;\">\\(\\phantom{\\rule{3.8em}{0ex}}4=4\\)\u2713<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Is their sum 1?<\/td>\n<td style=\"width: 50%;\">\\(\\phantom{\\rule{1.5em}{0ex}}-3+4\\stackrel{?}{=}1\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<td style=\"width: 50%;\">\\(\\phantom{\\rule{3.8em}{0ex}}1=1\\)\u2713<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"width: 50%; height: 30px;\">The numbers are \u22123 and \u22124.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344254538\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344254541\" data-type=\"exercise\">\n<div id=\"fs-id1168344285604\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344285604\" data-type=\"problem\">\n<p id=\"fs-id1168344285606\">One number is eight more than twice another. Their sum is negative four. Find the numbers.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344125501\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344125503\">\\(-4,0\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344330486\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344308700\" data-type=\"exercise\">\n<div id=\"fs-id1168344308702\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344308702\" data-type=\"problem\">\n<p id=\"fs-id1168344308704\">One number is three more than three times another. Their sum is \\(-5\\). Find the numbers.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344298821\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344298823\">\\(-3,-2\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344319176\">Some number problems involve consecutive integers.<em data-effect=\"italics\">Consecutive integers<\/em> are integers that immediately follow each other.<\/p>\n\u00a0Examples of consecutive integers are:\n\n\\(\\begin{array}{c}1,2,3,4\\hfill \\\\ \\\\ -10,-9,-8,-7\\hfill \\\\ 150,151,152,153\\hfill \\end{array}\\)\n<p id=\"fs-id1168344327961\">Notice that each number is one more than the number preceding it. So if we define the first integer as <em data-effect=\"italics\">n<\/em>, the next consecutive integer is \\(n+1\\). The one after that is one more than \\(n+1\\), so it is \\(n+1+1\\), which is \\(n+2\\).<\/p>\n\\(\\begin{array}{cccc}\\hfill n\\hfill &amp; &amp; &amp; {1}^{\\text{st}}\\phantom{\\rule{0.2em}{0ex}}\\text{integer}\\hfill \\\\ \\hfill n+1\\hfill &amp; &amp; &amp; {2}^{\\text{nd}}\\phantom{\\rule{0.2em}{0ex}}\\text{consecutive integer}\\hfill \\\\ \\hfill n+2\\hfill &amp; &amp; &amp; {3}^{\\text{rd}}\\phantom{\\rule{0.2em}{0ex}}\\text{consecutive integer . . . etc.}\\hfill \\end{array}\\)\n<div id=\"fs-id1168344249461\" class=\"bc-section section\" data-depth=\"1\">\n<div data-type=\"equation\" data-label=\"\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344296047\" data-type=\"problem\">\n<p id=\"fs-id1168344296049\">The sum of two consecutive integers is 47. Find the numbers.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344296053\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 2. Identify<\/strong> what you are looking for.<\/td>\n<td style=\"width: 50%;\">two consecutive integers<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 3. Name<\/strong> each number.<\/td>\n<td style=\"width: 50%;\">Let \\(n={1}^{\\mathrm{st}}\\) integer.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(n+1=\\) next consecutive integer<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 4. Translate. <\/strong><\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Restate as one sentence.<\/td>\n<td style=\"width: 50%;\">The sum of the integers is 47.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Translate into an equation.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167270257414\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_013a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167270256828\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_013b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Combine like terms.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167269983541\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_013c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Subtract 1 from each side.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167261209602\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_013d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Divide each side by 2.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167270290555\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_013e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167263494184\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_013f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167269975642\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_013g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167269972879\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_013h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 6. Check.<\/strong><\/td>\n<td style=\"width: 50%;\">\\(\\begin{array}{ccc}\\hfill 23+24&amp; \\stackrel{?}{=}\\hfill &amp; 47\\hfill \\\\ \\hfill 47&amp; =\\hfill &amp; 47\\checkmark\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"width: 50%;\">The two consecutive integers are 23 and 24.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344281852\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344308176\" data-type=\"exercise\">\n<div id=\"fs-id1168344308178\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344308178\" data-type=\"problem\">\n<p id=\"fs-id1168344308180\">The sum of two consecutive integers is \\(95\\). Find the numbers.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344281649\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344281651\">47, 48<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344281658\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344281661\" data-type=\"exercise\">\n<div id=\"fs-id1168344281663\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344281663\" data-type=\"problem\">\n<p id=\"fs-id1168344281665\">The sum of two consecutive integers is \\(-31\\). Find the numbers.<\/p>\n\n<\/div>\n<div id=\"fs-id1168344250051\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344250053\">\\(-16,-15\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344286019\" data-type=\"problem\">\n<p id=\"fs-id1168344286021\">Find three consecutive integers whose sum is \\(-42\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168344286032\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td style=\"width: 50%;\">three consecutive integers<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 3. Name<\/strong> each of the three numbers.<\/td>\n<td style=\"width: 50%;\">Let \\(n={1}^{\\mathrm{st}}\\) integer.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(n+1=\\) 2<sup>nd<\/sup> consecutive integer<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(n+2=\\) 3<sup>rd<\/sup> consecutive integer<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 4. Translate. <\/strong><\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Restate as one sentence.<\/td>\n<td style=\"width: 50%;\">The sum of the three integers is \u221242.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Translate into an equation.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167268280403\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167266954802\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Combine like terms.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167266954810\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Subtract 3 from each side.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271093107\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Divide each side by 3.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271070796\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271016239\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271181140\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167270951708\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271234318\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167270916307\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167267549035\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 6. Check.<\/strong><\/td>\n<td style=\"width: 50%;\">\\(\\begin{array}{ccc}\\hfill -13+\\left(-14\\right)+\\left(-15\\right)&amp; \\stackrel{?}{=}\\hfill &amp; -42\\hfill \\\\ \\hfill -42&amp; =\\hfill &amp; -42\\checkmark\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"width: 50%;\">The three consecutive integers are \u221213, \u221214, and \u221215.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344319103\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344319106\" data-type=\"exercise\">\n<div id=\"fs-id1168344319108\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344319108\" data-type=\"problem\">\n<p id=\"fs-id1168344278804\">Find three consecutive integers whose sum is \\(-96\\).<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344278816\">\\(-33,-32,-31\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344297618\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344297621\" data-type=\"exercise\">\n<div id=\"fs-id1168344297624\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344297624\" data-type=\"problem\">\n<p id=\"fs-id1168344297626\">Find three consecutive integers whose sum is \\(-36\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168344297636\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344297638\">\\(-13,-12,-11\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344249061\">Now that we have worked with consecutive integers, we will expand our work to include consecutive even integers and consecutive odd integers. <em data-effect=\"italics\">Consecutive even integers<\/em> are even integers that immediately follow one another. Examples of consecutive even integers are:<\/p>\n\\(\\begin{array}{c}18,20,22\\hfill \\\\ \\\\ 64,66,68\\hfill \\\\ -12,-10,-8\\hfill \\end{array}\\)\n<p id=\"fs-id1168344246163\">Notice each integer is 2 more than the number preceding it. If we call the first one <em data-effect=\"italics\">n<\/em>, then the next one is \\(n+2\\). The next one would be \\(n+2+2\\) or \\(n+4\\).<\/p>\n\\(\\begin{array}{cccc}\\hfill n\\hfill &amp; &amp; &amp; {1}^{\\text{st}}\\phantom{\\rule{0.2em}{0ex}}\\text{even integer}\\hfill \\\\ \\hfill n+2\\hfill &amp; &amp; &amp; {2}^{\\text{nd}}\\phantom{\\rule{0.2em}{0ex}}\\text{consecutive even integer}\\hfill \\\\ \\hfill n+4\\hfill &amp; &amp; &amp; {3}^{\\text{rd}}\\phantom{\\rule{0.2em}{0ex}}\\text{consecutive even integer . . . etc.}\\hfill \\end{array}\\)\n<p id=\"fs-id1168344302427\"><em data-effect=\"italics\">Consecutive odd integers<\/em> are odd integers that immediately follow one another. Consider the consecutive odd integers 77, 79, and 81<\/p>\n\\(\\begin{array}{c}77,79,81\\hfill \\\\ \\\\ n,n+2,n+4\\hfill \\end{array}\\)\n\n\\(\\begin{array}{cccc}\\hfill n\\hfill &amp; &amp; &amp; {1}^{\\text{st}}\\phantom{\\rule{0.2em}{0ex}}\\text{odd integer}\\hfill \\\\ \\hfill n+2\\hfill &amp; &amp; &amp; {2}^{\\text{nd}}\\phantom{\\rule{0.2em}{0ex}}\\text{consecutive odd integer}\\hfill \\\\ \\hfill n+4\\hfill &amp; &amp; &amp; {3}^{\\text{rd}}\\phantom{\\rule{0.2em}{0ex}}\\text{consecutive odd integer . . . etc.}\\hfill \\end{array}\\)\n<p id=\"fs-id1168344306541\">Does it seem strange to add 2 (an even number) to get from one odd integer to the next? Do you get an odd number or an even number when we add 2 to 3? to 11? to 47?<\/p>\n<p id=\"fs-id1168344306546\">Whether the problem asks for consecutive even numbers or odd numbers, you don\u2019t have to do anything different. The pattern is still the same\u2014to get from one odd or one even integer to the next, add 2<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344306557\" data-type=\"problem\">\n<p id=\"fs-id1168344306560\">Find three consecutive even integers whose sum is 84<\/p>\n\n<\/div>\n<div id=\"fs-id1168344306564\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-57\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td style=\"width: 204.406px;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"width: 448.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\"><strong>Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td style=\"width: 448.406px;\">three consecutive even integers<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\"><strong>Step 3. Name<\/strong> the integers.<\/td>\n<td style=\"width: 448.406px;\">Let \\(n={1}^{\\text{st}}\\) even integer.\n\\(n+2={2}^{\\text{nd}}\\) consecutive even integer\n\\(n+4={3}^{\\text{rd}}\\) consecutive even integer<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\"><strong>Step 4. Translate.<\/strong><\/td>\n<td style=\"width: 448.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\">Restate as one sentence.<\/td>\n<td style=\"width: 448.406px;\">The sume of the three even integers is 84.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\">Translate into an equation.<\/td>\n<td style=\"width: 448.406px;\">\\(n+n+2+n+4\\phantom{\\rule{0.2em}{0ex}}=\\phantom{\\rule{0.2em}{0ex}}84\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"width: 448.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\">Combine like terms.<\/td>\n<td style=\"width: 448.406px;\">\\(n+n+2+n+4\\phantom{\\rule{0.2em}{0ex}}=\\phantom{\\rule{0.2em}{0ex}}84\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\">Subtract 6 from each side.<\/td>\n<td style=\"width: 448.406px;\">\\(3n+6\\phantom{\\rule{0.2em}{0ex}}=\\phantom{\\rule{0.2em}{0ex}}84\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\">Divide each side by 3.<\/td>\n<td style=\"width: 448.406px;\">\\(3n\\phantom{\\rule{0.2em}{0ex}}=\\phantom{\\rule{0.2em}{0ex}}78\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\"><\/td>\n<td style=\"width: 448.406px;\">\\(\\begin{array}{cc}n=26&amp; {1}^{\\text{st}}\\phantom{\\rule{0.2em}{0ex}}\\text{integer}\\\\ \\\\ n+2&amp; {2}^{\\text{nd}}\\phantom{\\rule{0.2em}{0ex}}\\text{integer}\\\\ 26+2&amp; \\\\ 28&amp; \\\\ \\\\ n+4&amp; {3}^{\\text{rd}}\\phantom{\\rule{0.2em}{0ex}}\\text{integer}\\\\ 26+4&amp; \\\\ 30&amp; \\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\"><strong>Step 6. Check.<\/strong><\/td>\n<td style=\"width: 448.406px;\">\\(\\begin{array}{c}26+28+30\\stackrel{?}{=}84\\\\ 84=84\\checkmark\\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"width: 448.406px;\">The three consecutive integers are 26, 28, and 30.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344334628\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344334632\" data-type=\"exercise\">\n<div id=\"fs-id1168344334634\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344334634\" data-type=\"problem\">\n<p id=\"fs-id1168344334636\">Find three consecutive even integers whose sum is 102<\/p>\n\n<\/div>\n<div id=\"fs-id1168344334640\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344334643\">32, 34, 36<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344297579\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344297582\" data-type=\"exercise\">\n<div id=\"fs-id1168344297584\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344297584\" data-type=\"problem\">\n<p id=\"fs-id1168344297586\">Find three consecutive even integers whose sum is \\(-24\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168344297597\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344297599\">\\(-10,-8,-6\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344126231\" data-type=\"problem\">\n<p id=\"fs-id1168344126233\">A married couple together earns \\$110,000 a year. The wife earns \\$16,000 less than twice what her husband earns. What does the husband earn?<\/p>\n\n<\/div>\n<div id=\"fs-id1168344126239\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td style=\"width: 50%;\">How much does the husband earn?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 3. Name<\/strong>.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Choose a variable to represent the amount\nthe husband earns.<\/td>\n<td style=\"width: 50%;\">Let \\(h=\\) the amount the husband earns.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">The wife earns \\$16,000 less than twice that.<\/td>\n<td style=\"width: 50%;\">\\(2h-16,000\\) the amount the wife earns.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 4. Translate. <\/strong><\/td>\n<td style=\"width: 50%;\">Together the husband and wife earn \\$110,000.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Restate the problem in one sentence with\nall the important information.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271070928\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_015a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Translate into an equation.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271070945\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_015b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"width: 50%;\">h + 2h \u2212 16,000 = 110,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Combine like terms.<\/td>\n<td style=\"width: 50%;\">\\(\\phantom{\\rule{1.1em}{0ex}}\\)3h \u2212 16,000 = 110,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Add 16,000 to both sides and simplify.<\/td>\n<td style=\"width: 50%;\">\\(\\phantom{\\rule{4.7em}{0ex}}\\)3h = 126,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Divide each side by 3.<\/td>\n<td style=\"width: 50%;\">\\(\\phantom{\\rule{5.2em}{0ex}}\\)h = 42,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\phantom{\\rule{6.2em}{0ex}}\\)\\$42,000\u2003amount husband earns<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\phantom{\\rule{4.7em}{0ex}}\\)2h \u2212 16,000\u2003amount wife earns<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\phantom{\\rule{1.88em}{0ex}}\\)2(42,000) \u2212 16,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\phantom{\\rule{3.05em}{0ex}}\\)84,000 \u2212 16,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\phantom{\\rule{6.85em}{0ex}}\\)68,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 6. Check.<\/strong><\/td>\n<td style=\"width: 50%;\">If the wife earns \\$68,000 and the husband earns \\$42,000 is the total \\$110,000? Yes!<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"width: 50%;\">The husband earns \\$42,000 a year.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344126257\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344332527\" data-type=\"exercise\">\n<div id=\"fs-id1168344332530\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344332530\" data-type=\"problem\">\n<p id=\"fs-id1168344332532\">According to the National Automobile Dealers Association, the average cost of a car in 2014 was 28,500. This was 1,500 less than 6 times the cost in 1975. What was the average cost of a car in 1975?<\/p>\n\n<\/div>\n<div id=\"fs-id1168344332538\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344332540\">5,000<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344332546\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344338480\" data-type=\"exercise\">\n<div id=\"fs-id1168344338483\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344338483\" data-type=\"problem\">\n<p id=\"fs-id1168344338485\">The Canadian Real Estate Association (CREA) data shows that the median price of new home in the Canada in December 2018 was \\$470,000. This was \\$14,000 more than 19 times the price in December 1967. What was the median price of a new home in December 1967?<\/p>\n\n<\/div>\n<div id=\"fs-id1168344338491\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344338493\">\\$24,000<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"fs-id1171791390945\" data-bullet-style=\"bullet\">\n \t<li><strong data-effect=\"bold\">Problem-Solving Strategy<\/strong>\n<ol id=\"fs-id1167265385253\" class=\"stepwise\" type=\"1\">\n \t<li><strong data-effect=\"bold\">Read<\/strong> the problem. Make sure all the words and ideas are understood.<\/li>\n \t<li><strong data-effect=\"bold\">Identify<\/strong> what we are looking for.<\/li>\n \t<li><strong data-effect=\"bold\">Name<\/strong> what we are looking for. Choose a variable to represent that quantity.<\/li>\n \t<li><strong data-effect=\"bold\">Translate<\/strong> into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.<\/li>\n \t<li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li>\n \t<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\n \t<li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/li>\n \t<li><strong data-effect=\"bold\">Consecutive Integers<\/strong>\nConsecutive integers are integers that immediately follow each other.\n<div id=\"fs-id1168345325923\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccc}\\hfill n\\hfill &amp; &amp; &amp; {1}^{\\text{st}}\\phantom{\\rule{0.2em}{0ex}}\\text{integer}\\hfill \\\\ \\hfill n+1\\hfill &amp; &amp; &amp; {2}^{\\text{nd}}\\phantom{\\rule{0.2em}{0ex}}\\text{integer consecutive integer}\\hfill \\\\ \\hfill n+2\\hfill &amp; &amp; &amp; {3}^{\\text{rd}}\\phantom{\\rule{0.2em}{0ex}}\\text{consecutive integer . . . etc.}\\hfill \\end{array}\\)<\/div>\nConsecutive even integers are even integers that immediately follow one another.\n<div id=\"fs-id1168345397558\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccc}\\hfill n\\hfill &amp; &amp; &amp; {1}^{\\text{st}}\\phantom{\\rule{0.2em}{0ex}}\\text{integer}\\hfill \\\\ \\hfill n+2\\hfill &amp; &amp; &amp; {2}^{\\text{nd}}\\phantom{\\rule{0.2em}{0ex}}\\text{integer consecutive integer}\\hfill \\\\ \\hfill n+4\\hfill &amp; &amp; &amp; {3}^{\\text{rd}}\\phantom{\\rule{0.2em}{0ex}}\\text{consecutive integer . . . etc.}\\hfill \\end{array}\\)<\/div>\nConsecutive odd integers are odd integers that immediately follow one another.\n<div id=\"fs-id1168341958730\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccc}\\hfill n\\hfill &amp; &amp; &amp; {1}^{\\text{st}}\\phantom{\\rule{0.2em}{0ex}}\\text{integer}\\hfill \\\\ \\hfill n+2\\hfill &amp; &amp; &amp; {2}^{\\text{nd}}\\phantom{\\rule{0.2em}{0ex}}\\text{integer consecutive integer}\\hfill \\\\ \\hfill n+4\\hfill &amp; &amp; &amp; {3}^{\\text{rd}}\\phantom{\\rule{0.2em}{0ex}}\\text{consecutive integer . . . etc.}\\hfill \\end{array}\\)<\/div><\/li>\n<\/ul>\n<h1 data-type=\"title\">Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1168344285166\">Use the Approach Word Problems with a Positive Attitude<\/h2>\n<p id=\"fs-id1166424888146\">In the following exercises, prepare the lists described.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 156px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 62px;\">\n<td style=\"width: 50%; height: 62px;\">1. List five positive thoughts you can say to yourself that will help you approach word problems with a positive attitude. You may want to copy them on a sheet of paper and put it in the front of your notebook, where you can read them often.<\/td>\n<td style=\"width: 50%; height: 62px;\">2. List five negative thoughts that you have said to yourself in the past that will hinder your progress on word problems. You may want to write each one on a small piece of paper and rip it up to symbolically destroy the negative thoughts.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1168344337083\">Use a Problem-Solving Strategy for Word Problems<\/h2>\n<p id=\"fs-id1166424884530\">In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">3. Two-thirds of the children in the fourth-grade class are girls. If there are 20 girls, what is the total number of children in the class?<\/td>\n<td style=\"width: 50%;\">4. Three-fifths of the members of the school choir are women. If there are 24 women, what is the total number of choir members?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">5. Zachary has 25 country music CDs, which is one-fifth of his CD collection. How many CDs does Zachary have?<\/td>\n<td style=\"width: 50%;\">6. One-fourth of the candies in a bag of M&amp;M\u2019s are red. If there are 23 red candies, how many candies are in the bag?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">7. There are 16 girls in a school club. The number of girls is four more than twice the number of boys. Find the number of boys.<\/td>\n<td style=\"width: 50%;\">8. There are 18 Cub Scouts in Pack 645. The number of scouts is three more than five times the number of adult leaders. Find the number of adult leaders.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">9. Huong is organizing paperback and hardback books for her club\u2019s used book sale. The number of paperbacks is 12 less than three times the number of hardbacks. Huong had 162 paperbacks. How many hardback books were there?<\/td>\n<td style=\"width: 50%;\">10. Jeff is lining up children\u2019s and adult bicycles at the bike shop where he works. The number of children\u2019s bicycles is nine less than three times the number of adult bicycles. There are 42 adult bicycles. How many children\u2019s bicycles are there?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">11. Philip pays \\$1,620 in rent every month. This amount is \\$120 more than twice what his brother Paul pays for rent. How much does Paul pay for rent?<\/td>\n<td style=\"width: 50%;\">12. Marc just bought an SUV for \\$54,000. This is \\$7,400 less than twice what his wife paid for her car last year. How much did his wife pay for her car?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">13. Laurie has \\$46,000 invested in stocks and bonds. The amount invested in stocks is \\$8,000 less than three times the amount invested in bonds. How much does Laurie have invested in bonds?<\/td>\n<td style=\"width: 50%;\">14. Erica earned a total of \\$50,450 last year from her two jobs. The amount she earned from her job at the store was \\$1,250 more than three times the amount she earned from her job at the college. How much did she earn from her job at the college?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1168344292961\">Solve Number Problems<\/h2>\n<p id=\"fs-id1166425001516\">In the following exercises, solve each number word problem.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">15. The sum of a number and eight is 12. Find the number.<\/td>\n<td style=\"width: 50%;\">16. The sum of a number and nine is 17. Find the number.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">17. The difference of a number and 12 is three. Find the number.<\/td>\n<td style=\"width: 50%;\">18. The difference of a number and eight is four. Find the number.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">19. The sum of three times a number and eight is 23. Find the number.<\/td>\n<td style=\"width: 50%;\">20. The sum of twice a number and six is 14. Find the number.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">21.The difference of twice a number and seven is 17. Find the number.<\/td>\n<td style=\"width: 50%;\">22. The difference of four times a number and seven is 21. Find the number.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">23. Three times the sum of a number and nine is 12. Find the number.<\/td>\n<td style=\"width: 50%;\">24. Six times the sum of a number and eight is 30. Find the number.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">25. One number is six more than the other. Their sum is 42. Find the numbers.<\/td>\n<td style=\"width: 50%;\">26. One number is five more than the other. Their sum is 33. Find the numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">27. The sum of two numbers is 20. One number is four less than the other. Find the numbers.<\/td>\n<td style=\"width: 50%;\">28. The sum of two numbers is 27. One number is seven less than the other. Find the numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">29. The sum of two numbers is \\(-45\\). One number is nine more than the other. Find the numbers.<\/td>\n<td style=\"width: 50%;\">30. The sum of two numbers is \\(-61\\). One number is 35 more than the other. Find the numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">31. The sum of two numbers is \\(-316\\). One number is 94 less than the other. Find the numbers.<\/td>\n<td style=\"width: 50%;\">32. The sum of two numbers is \\(-284\\). One number is 62 less than the other. Find the numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">33. One number is 14 less than another. If their sum is increased by seven, the result is 85. Find the numbers.<\/td>\n<td style=\"width: 50%;\">34. One number is 11 less than another. If their sum is increased by eight, the result is 71. Find the numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">35. One number is five more than another. If their sum is increased by nine, the result is 60. Find the numbers.<\/td>\n<td style=\"width: 50%;\">36. One number is eight more than another. If their sum is increased by 17, the result is 95. Find the numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">37. One number is one more than twice another. Their sum is \\(-5\\). Find the numbers.<\/td>\n<td style=\"width: 50%;\">38. One number is six more than five times another. Their sum is six. Find the numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">39. The sum of two numbers is 14. One number is two less than three times the other. Find the numbers.<\/td>\n<td style=\"width: 50%;\">40. The sum of two numbers is zero. One number is nine less than twice the other. Find the numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">41. The sum of two consecutive integers is 77. Find the integers.<\/td>\n<td style=\"width: 50%;\">42. The sum of two consecutive integers is 89. Find the integers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">43. The sum of two consecutive integers is \\(-23\\). Find the integers.<\/td>\n<td style=\"width: 50%;\">44. The sum of two consecutive integers is \\(-37\\). Find the integers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">45. The sum of three consecutive integers is 78. Find the integers.<\/td>\n<td style=\"width: 50%;\">46. The sum of three consecutive integers is 60. Find the integers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">47. Find three consecutive integers whose sum is \\(-36\\).<\/td>\n<td style=\"width: 50%;\">48. Find three consecutive integers whose sum is \\(-3\\).<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">49. Find three consecutive even integers whose sum is 258.<\/td>\n<td style=\"width: 50%;\">50. Find three consecutive even integers whose sum is 222.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">51. Find three consecutive odd integers whose sum is 171.<\/td>\n<td style=\"width: 50%;\">52. Find three consecutive odd integers whose sum is 291.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">53. Find three consecutive even integers whose sum is \\(-36\\).<\/td>\n<td style=\"width: 50%;\">54. Find three consecutive even integers whose sum is \\(-84\\).<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">55. Find three consecutive odd integers whose sum is \\(-213\\).<\/td>\n<td style=\"width: 50%;\">56. Find three consecutive odd integers whose sum is \\(-267\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3 data-type=\"title\">Everyday Math<\/h3>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">57.<strong data-effect=\"bold\"> Sale Price.<\/strong> Patty paid \\$35 for a purse on sale for \\$10 off the original price. What was the original price of the purse?<\/td>\n<td style=\"width: 50%;\">58.<strong data-effect=\"bold\"> Sale Price.<\/strong> Travis bought a pair of boots on sale for \\$25 off the original price. He paid \\$60 for the boots. What was the original price of the boots?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">59.<strong data-effect=\"bold\"> Buying in Bulk.<\/strong> Minh spent \\$6.25 on five sticker books to give his nephews. Find the cost of each sticker book.<\/td>\n<td style=\"width: 50%;\">60.<strong data-effect=\"bold\"> Buying in Bulk.<\/strong> Alicia bought a package of eight peaches for \\$3.20. Find the cost of each peach.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">61.<strong data-effect=\"bold\"> Price before Sales Tax.<\/strong> Tom paid \\$1,166.40 for a new refrigerator, including \\$86.40 tax. What was the price of the refrigerator?<\/td>\n<td style=\"width: 50%;\">62.<strong data-effect=\"bold\"> Price before Sales Tax.<\/strong> Kenji paid \\$2,279 for a new living room set, including \\$129 tax. What was the price of the living room set?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3 data-type=\"title\">Writing Exercises<\/h3>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">63. What has been your past experience solving word problems?<\/td>\n<td style=\"width: 50%;\">64. When you start to solve a word problem, how do you decide what to let the variable represent?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">65. What are consecutive odd integers? Name three consecutive odd integers between 50 and 60.<\/td>\n<td style=\"width: 50%;\">66. What are consecutive even integers? Name three consecutive even integers between \\(-50\\) and \\(-40\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 192px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">1. Answers will vary<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">3. 30<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">5. 125<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">7. 6<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">9. 58<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">11. \\$750<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">13. \\$13,500<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">15. 4<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">17. 15<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">19. 5<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">21. 12<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">23. \\(-5\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">25. 18, 24<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">27. 8, 12<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">29. \\(-18,-27\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">31. \\(-111,-205\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">33. 32, 46<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">35. 23, 28<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">37. \\(-2,-3\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">39. 4, 10<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">41. 38, 39<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">43. \\(-11,-12\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">45. 25, 26, 27<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">47. \\(-11,-12,-13\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">49. 84, 86, 88<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">51. 55, 57, 59<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">53. \\(-10,-12,-14\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">55. \\(-69,-71,-73\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">57. \\$45<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">59. \\$1.25<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">61. \\$1080<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">63. Answers will vary<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">65. Consecutive odd integers are odd numbers that immediately follow each other. An example of three consecutive odd integers between 50 and 60 would be 51, 53, and 55.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cUse a Problem-Solving Strategy\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Approach word problems with a positive attitude<\/li>\n<li>Use a problem-solving strategy for word problems<\/li>\n<li>Solve number problems<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Approach Word Problems with a Positive Attitude<\/h1>\n<p id=\"fs-id1168344306748\">\u201cIf you think you can\u2026 or think you can\u2019t\u2026 you\u2019re right.\u201d\u2014Henry Ford<\/p>\n<p id=\"fs-id1168344156191\">The world is full of word problems! Will my income qualify me to rent that apartment? How much punch do I need to make for the party? What size diamond can I afford to buy my girlfriend? Should I fly or drive to my family reunion?<\/p>\n<p id=\"fs-id1168344196663\">How much money do I need to fill the car with gas? How much tip should I leave at a restaurant? How many socks should I pack for vacation? What size turkey do I need to buy for Thanksgiving dinner, and then what time do I need to put it in the oven? If my sister and I buy our mother a present, how much does each of us pay?<\/p>\n<p id=\"fs-id1168344337114\">Now that we can solve equations, we are ready to apply our new skills to word problems. Do you know anyone who has had negative experiences in the past with word problems? Have you ever had thoughts like the student below?<\/p>\n<div id=\"CNX_ElemAlg_Figure_03_01_002\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">Negative thoughts can be barriers to success.<\/div>\n<figure style=\"width: 627px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/07\/CNX_ElemAlg_Figure_03_01_002_img_new.jpg\" alt=\"A student is shown with thought bubbles saying \u201cI don\u2019t know whether to add, subtract, multiply, or divide!,\u201d \u201cI don\u2019t understand word problems!,\u201d \u201cMy teachers never explained this!,\u201d \u201cIf I just skip all the word problems, I can probably still pass the class,\u201d and \u201cI just can\u2019t do this!\u201d\" width=\"627\" height=\"422\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .1<\/figcaption><\/figure>\n<\/div>\n<p id=\"fs-id1168344164823\">When we feel we have no control, and continue repeating negative thoughts, we set up barriers to success. We need to calm our fears and change our negative feelings.<\/p>\n<p id=\"fs-id1168344117014\">Start with a fresh slate and begin to think positive thoughts. If we take control and believe we can be successful, we will be able to master word problems! Read the positive thoughts in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_03_01_003\">(Figure 2)<\/a> and say them out loud.<\/p>\n<div id=\"CNX_ElemAlg_Figure_03_01_003\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">Thinking positive thoughts is a first step towards success.<\/div>\n<figure style=\"width: 593px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_003.jpg\" alt=\"A student is shown with thought bubbles saying \u201cWhile word problems were hard in the past, I think I can try them now,\u201d \u201cI am better prepared now. I think I will begin to understand word problems,\u201d \u201cI think I can! I think I can!,\u201d and \u201cIt may take time, but I can begin to solve word problems.\u201d\" width=\"593\" height=\"426\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .2<\/figcaption><\/figure>\n<\/div>\n<p id=\"fs-id1168344198246\">Think of something, outside of school, that you can do now but couldn\u2019t do 3 years ago. Is it driving a car? Snowboarding? Cooking a gourmet meal? Speaking a new language? Your past experiences with word problems happened when you were younger\u2014now you\u2019re older and ready to succeed!<\/p>\n<h1 data-type=\"title\">Use a Problem-Solving Strategy for Word Problems<\/h1>\n<p id=\"fs-id1168344342341\">We have reviewed translating English phrases into algebraic expressions, using some basic mathematical vocabulary and symbols. We have also translated English sentences into algebraic equations and solved some word problems. The word problems applied math to everyday situations. We restated the situation in one sentence, assigned a variable, and then wrote an equation to solve the problem. This method works as long as the situation is familiar and the math is not too complicated.<\/p>\n<p id=\"fs-id1168344254595\">Now, we\u2019ll expand our strategy so we can use it to successfully solve any word problem. We\u2019ll list the strategy here, and then we\u2019ll use it to solve some problems. We summarize below an effective strategy for problem solving.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Use a Problem-Solving Strategy to Solve Word Problems.<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1166424800382\" class=\"stepwise\" type=\"1\">\n<li><strong data-effect=\"bold\">Read<\/strong> the problem. Make sure all the words and ideas are understood.<\/li>\n<li><strong data-effect=\"bold\">Identify<\/strong> what we are looking for.<\/li>\n<li><strong data-effect=\"bold\">Name<\/strong> what we are looking for. Choose a variable to represent that quantity.<\/li>\n<li><strong data-effect=\"bold\">Translate<\/strong> into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebraic equation.<\/li>\n<li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li>\n<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\n<li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344229115\" class=\"howto\" data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344286696\" data-type=\"problem\">\n<p id=\"fs-id1168344191428\">Pilar bought a purse on sale for &#36;18, which is one-half of the original price. What was the original price of the purse?<\/p>\n<\/div>\n<div id=\"fs-id1168344117081\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168344074298\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem. Read the problem two or more times if necessary. Look up any unfamiliar words in a dictionary or on the internet.<\/p>\n<ul id=\"fs-id1166424861466\" data-bullet-style=\"bullet\">\n<li><em data-effect=\"italics\">In this problem, is it clear what is being discussed? Is every word familiar?<\/em><\/li>\n<\/ul>\n<p id=\"fs-id1168344164753\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for. Did you ever go into your bedroom to get something and then forget what you were looking for? It\u2019s hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!<\/p>\n<ul id=\"fs-id1166424917531\" data-bullet-style=\"bullet\">\n<li><em data-effect=\"italics\">In this problem, the words \u201cwhat was the original price of the purse\u201d tell us what we need to find.<\/em><\/li>\n<\/ul>\n<p id=\"fs-id1168344318843\"><strong data-effect=\"bold\">Step 3. Name<\/strong> what we are looking for. Choose a variable to represent that quantity. We can use any letter for the variable, but choose one that makes it easy to remember what it represents.<\/p>\n<ul id=\"fs-id1166424772657\" data-bullet-style=\"bullet\">\n<li>Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-159263f1bfd0df93391450a8fb398ebc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"28\" style=\"vertical-align: -4px;\" \/> the original price of the purse.<\/li>\n<\/ul>\n<p id=\"fs-id1168344229632\"><strong data-effect=\"bold\">Step 4. Translate<\/strong> into an equation. It may be helpful to restate the problem in one sentence with all the important information. Translate the English sentence into an algebraic equation.<\/p>\n<p id=\"fs-id1168344298465\">Reread the problem carefully to see how the given information is related. Often, there is one sentence that gives this information, or it may help to write one sentence with all the important information. Look for clue words to help translate the sentence into algebra. Translate the sentence into an equation.<\/p>\n<table id=\"eip-id1167269958572\" style=\"width: 100%;\" summary=\"We are given the direction to restate the problem in one sentence with all the important information. To the right of this, we have 18 is one-half the original price. Below this, we are told to translate this into an equation. Hence we have 18 equals 1\/2 times p.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Restate the problem in one sentence with all the important information.<\/td>\n<td><span id=\"eip-id1167265664116\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_004a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Translate into an equation.<\/td>\n<td><span id=\"eip-id1167265757342\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_004b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344281297\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation using good algebraic techniques. Even if you know the solution right away, using good algebraic techniques here will better prepare you to solve problems that do not have obvious answers.<\/p>\n<table id=\"eip-id1167269971537\" style=\"width: 100%;\" summary=\"We are given the direction to restate the problem in one sentence with all the important information. To the right of this, we have 18 is one-half the original price. Below this, we are told to translate this into an equation. Hence we have 18 equals 1\/2 times p.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Solve the equation.<\/td>\n<td><span id=\"eip-id1167270176483\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_005a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by 2.<\/td>\n<td><span id=\"eip-id1167265367934\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_005b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1167266374820\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_005c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344155673\"><strong data-effect=\"bold\">Step 6. Check<\/strong> the answer in the problem to make sure it makes sense. We solved the equation and found that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0b5529054bdd827e0a69f9dbbd28be8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"52\" style=\"vertical-align: -4px;\" \/>, which means \u201cthe original price\u201d was &#36;36<\/p>\n<ul id=\"fs-id1166424777751\" data-bullet-style=\"bullet\">\n<li><em data-effect=\"italics\">Does &#36;36 make sense in the problem? Yes, because 18 is one-half of 36, and the purse was on sale at half the original price.<\/em><\/li>\n<\/ul>\n<p id=\"fs-id1168344087441\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question with a complete sentence. The problem asked \u201cWhat was the original price of the purse?\u201d<\/p>\n<ul id=\"fs-id1166424844683\" data-bullet-style=\"bullet\">\n<li><em data-effect=\"italics\">The answer to the question is: \u201cThe original price of the purse was &#36;36.\u201d<\/em><\/li>\n<\/ul>\n<p id=\"fs-id1168344247891\">If this were a homework exercise, our work might look like this:<\/p>\n<p id=\"fs-id1168344192192\">Pilar bought a purse on sale for &#36;18, which is one-half the original price. What was the original price of the purse?<\/p>\n<table id=\"eip-id1167270180122\" style=\"width: 100%;\" summary=\"We are told to let p equal the original price. Below this, we are told 18 is one-half the original price. To the right of this, we have 18 equals 1\/2 times p. Below this, we are told to check whether \ud83d\udcb236 is a reasonable price for a purse? The answer is yes. To the right of this, we have 2 times 18 equals 2 times 1\/2 times p. Then below this, we have 36 equals p. Below this, we are asked if 18 is one-half of 36. We have 18 equals with a question mark over it 1\/2 times 36. Below this, we have 18 equals 18.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 291px;\"><\/td>\n<td style=\"width: 264px;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-159263f1bfd0df93391450a8fb398ebc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"28\" style=\"vertical-align: -4px;\" \/> the original price.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 291px;\"><\/td>\n<td style=\"width: 264px;\">18 is one-half the original price.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 291px;\"><\/td>\n<td style=\"width: 264px;\"><span id=\"eip-id1167269978911\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_006a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 291px;\">Multiply both sides by 2.<\/td>\n<td style=\"width: 264px;\"><span id=\"eip-id1167261007231\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_006b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 291px;\">Simplify.<\/td>\n<td style=\"width: 264px;\"><span id=\"eip-id1167266207221\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_006c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 291px;\">Check. Is &#36;36 a reasonable price for a purse?<\/td>\n<td style=\"width: 264px;\">Yes.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 291px;\">Is 18 one half of 36?<\/td>\n<td style=\"width: 264px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-53c58d103093802f0f76a4bfd04d9f80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"82\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 291px;\"><\/td>\n<td style=\"width: 264px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17df5957655fb2895816115660273741_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#61;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"58\" style=\"vertical-align: 0px;\" \/>\u2713<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 291px;\"><\/td>\n<td style=\"width: 264px;\">The original price of the purse was &#36;36.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344295590\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344119591\" data-type=\"exercise\">\n<div id=\"fs-id1168344188976\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344188976\" data-type=\"problem\">\n<p id=\"fs-id1168344208579\">Joaquin bought a bookcase on sale for &#36;120, which was two-thirds of the original price. What was the original price of the bookcase?<\/p>\n<\/div>\n<div id=\"fs-id1168344227446\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344087983\">&#36;180<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344247292\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344330742\" data-type=\"exercise\">\n<div id=\"fs-id1168344313530\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344313530\" data-type=\"problem\">\n<p id=\"fs-id1168344341142\">Two-fifths of the songs in Mariel\u2019s playlist are country. If there are 16 country songs, what is the total number of songs in the playlist?<\/p>\n<\/div>\n<div id=\"fs-id1168344076283\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344334775\">40<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344249163\">Let\u2019s try this approach with another example.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344164632\" data-type=\"problem\">\n<p id=\"fs-id1168344188180\">Ginny and her classmates formed a study group. The number of girls in the study group was three more than twice the number of boys. There were 11 girls in the study group. How many boys were in the study group?<\/p>\n<\/div>\n<div id=\"fs-id1168344081872\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1167264182522\" style=\"height: 228px; width: 100%;\" summary=\"We are given a table with instructions on the left and mathematical statements on the right. It starts with Step 1. Read the problem. Then we have Step 2. Identify what we are looking for. To the right of this, we have \u201cHow many boys did he bring?\u201d Then we have Step 3. Name. Choose a variable to represent the number of boys. To the right of this, we let b equal the number of boys. Then we have Step 4. Translate. Restate the problem in one sentence with all the important information. To the right of this, we have The number of girls (11) was three more than twice the number of boys. Then, translate this into an equation, which gives 11 equals 2b plus 3. Then we have Step 5. Solve the equation. To the right of this, we have 11 equals 2b plus 3. We are told to subtract 3 from each side, so we have 11 minus 3 equals 2b plus 3 minus 3. We are told to simplify, which gives us 8 equals 2b. Then we are told to divide each side by 2, which gives 8\/2 equals 2b\/2. We are told to simplify, which gives 4 equals b. Then we have Step 6. Check. First, is our answer reasonable? Yes, having 4 boys in a study group seems OK. The problem says the number of girls was three more than twice the number of boys. If there are four boys, does that make eleven girls? Twice 4 boys is 8. Three more than 8 is 11. Finally, we have Step 7. Answer the question: \u201cThere were 4 boys in the study group.\u201d\" data-label=\"\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 337.406px;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"height: 14px; width: 315.406px;\"><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 337.406px;\"><strong>Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td style=\"height: 30px; width: 315.406px;\">How many boys were in the study group?<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 337.406px;\"><strong>Step 3. Name.<\/strong> Choose a variable to represent the number of boys.<\/td>\n<td style=\"height: 14px; width: 315.406px;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-602c4d5dfa06ccbd52974998a84a8f4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"29\" style=\"vertical-align: 0px;\" \/> the number of boys.<\/td>\n<\/tr>\n<tr style=\"height: 33px;\">\n<td style=\"height: 33px; width: 337.406px;\"><strong>Step 4. Translate.<\/strong> Restate the problem in one sentence with all the important information.<\/td>\n<td style=\"height: 33px; width: 315.406px;\"><span id=\"eip-id1167265328711\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 337.406px;\">Translate into an equation.<\/td>\n<td style=\"height: 14px; width: 315.406px;\"><span id=\"eip-id1167270022563\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_007b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 337.406px;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"height: 14px; width: 315.406px;\"><span id=\"eip-id1167269991276\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_007c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 337.406px;\">Subtract 3 from each side.<\/td>\n<td style=\"height: 14px; width: 315.406px;\"><span id=\"eip-id1167261207104\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_007d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 337.406px;\">Simplify.<\/td>\n<td style=\"height: 14px; width: 315.406px;\"><span id=\"eip-id1167261195902\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_007e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 337.406px;\">Divide each side by 2.<\/td>\n<td style=\"height: 23px; width: 315.406px;\"><span id=\"eip-id1167270244307\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_007f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 337.406px;\">Simplify.<\/td>\n<td style=\"height: 14px; width: 315.406px;\"><span id=\"eip-id1167269996886\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_007g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 337.406px;\"><strong>Step 6. Check.<\/strong> First, is our answer reasonable?<\/td>\n<td style=\"height: 30px; width: 315.406px;\">Yes, having 4 boys in a study group seems OK. The problem says the number of girls was 3 more than twice the number of boys. If there are four boys, does that make eleven girls? Twice 4 boys is 8. Three more than 8 is 11.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 337.406px;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"height: 14px; width: 315.406px;\">There were 4 boys in the study group.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344318972\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344162058\" data-type=\"exercise\">\n<div id=\"fs-id1168344285800\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344285800\" data-type=\"problem\">\n<p id=\"fs-id1168344083134\">Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was 3 more than twice the number of notebooks. He bought 7 textbooks. How many notebooks did he buy?<\/p>\n<\/div>\n<div id=\"fs-id1168344226688\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344207955\">2<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344248666\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344252987\" data-type=\"exercise\">\n<div id=\"fs-id1168344281885\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344281885\" data-type=\"problem\">\n<p id=\"fs-id1168344228250\">Gerry worked Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is eight more than twice the number of crossword puzzles. He completed 22 Sudoku puzzles. How many crossword puzzles did he do?<\/p>\n<\/div>\n<div id=\"fs-id1168344242946\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344125519\">7<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Solve Number Problems<\/h1>\n<p id=\"fs-id1168344126170\">Now that we have a problem solving strategy, we will use it on several different types of word problems. The first type we will work on is \u201cnumber problems.\u201d Number problems give some clues about one or more numbers. We use these clues to write an equation. Number problems don\u2019t usually arise on an everyday basis, but they provide a good introduction to practicing the problem solving strategy outlined above.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344213738\" data-type=\"problem\">\n<p id=\"fs-id1168344120473\">The difference of a number and six is 13. Find the number.<\/p>\n<\/div>\n<div id=\"fs-id1168344198836\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1167271015539\" style=\"width: 100%;\" summary=\"We are given a table with instructions on the left and mathematical statements on the right. It starts with Step 1. Read the problem. Are all the words familiar? Then we have Step 2. Identify what we are looking for. To the right of this, we have \u201cthe number.\u201d Then we have Step 3. Name. Choose a variable to represent the number. To the right of this, we let n equal the number. Then we have Step 4. Translate. Remember to look for clue words like \u201cdifference\u2026 of\u2026 and.\u201d Restate the problem as one sentence. To the right of this, we have The difference of the number and 6 is 13. Then, translate this into an equation, which gives n minus 6 equals 13. Then we have Step 5. Solve the equation. To the right of this, we have n minus 6 equals 13. We are told to simplify, which gives us n equals 19. Then we have Step 6. Check. The difference of 19 and 6 is 13. It checks! Finally, we have Step 7. Answer the question: \u201cThe number is 19.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><strong>Step 1. Read<\/strong> the problem. Are all the words familiar?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td>the number<\/td>\n<\/tr>\n<tr>\n<td><strong>Step 3. Name.<\/strong> Choose a variable to represent the number.<\/td>\n<td>Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-602c4d5dfa06ccbd52974998a84a8f4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"29\" style=\"vertical-align: 0px;\" \/> the number.<\/td>\n<\/tr>\n<tr>\n<td><strong>Step 4. Translate.<\/strong> Remember to look for clue words like &#8220;difference&#8230; of&#8230; and&#8230;&#8221;<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Restate the problem as one sentence.<\/td>\n<td><span id=\"eip-id1167267549086\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Translate into an equation.<\/td>\n<td><span id=\"eip-id1167267573042\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1167271354701\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_008c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"fs-id1169149211312\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_008d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><strong>Step 6. Check.<\/strong><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The difference of 19 and 6 is 13. It checks!<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td>The number is 19.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344196679\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344208705\" data-type=\"exercise\">\n<div id=\"fs-id1168344198937\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344198937\" data-type=\"problem\">\n<p id=\"fs-id1168344115069\">The difference of a number and eight is 17. Find the number.<\/p>\n<\/div>\n<div id=\"fs-id1168344102861\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344293018\">25<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344318146\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344306281\" data-type=\"exercise\">\n<div id=\"fs-id1168344306283\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344306283\" data-type=\"problem\">\n<p id=\"fs-id1168344332115\">The difference of a number and eleven is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00c6d30c5f7439a21caf981437f64be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/>. Find the number.<\/p>\n<\/div>\n<div id=\"fs-id1168344287715\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344342077\">4<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344254046\" data-type=\"problem\">\n<p id=\"fs-id1168344246247\">The sum of twice a number and seven is 15. Find the number.<\/p>\n<\/div>\n<div id=\"fs-id1168344208213\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1167268159009\" style=\"width: 100%;\" summary=\"We are given a table with instructions on the left and mathematical statements on the right. It starts with Step 1. Read the problem. Are all the words familiar? Then we have Step 2. Identify what we are looking for. To the right of this, we have \u201cthe number.\u201d Then we have Step 3. Name. Choose a variable to represent the number. To the right of this, we let n equal the number. Then we have Step 4. Translate. Remember to look for clue words like \u201cdifference\u2026 of\u2026 and.\u201d Restate the problem as one sentence. To the right of this, we have The difference of the number and 6 is 13. Then, translate this into an equation, which gives n minus 6 equals 13. Then we have Step 5. Solve the equation. To the right of this, we have n minus 6 equals 13. We are told to simplify, which gives us n equals 19. Then we have Step 6. Check. The difference of 19 and 6 is 13. It checks! Finally, we have Step 7. Answer the question: \u201cThe number is 19.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 366.406px;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"width: 286.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\"><strong>Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td style=\"width: 286.406px;\">the number<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\"><strong>Step 3. Name.<\/strong> Choose a variable to represent the number.<\/td>\n<td style=\"width: 286.406px;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-602c4d5dfa06ccbd52974998a84a8f4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"29\" style=\"vertical-align: 0px;\" \/> the number.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\"><strong>Step 4. Translate.<\/strong><\/td>\n<td style=\"width: 286.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\">Restate the problem as one sentence.<\/td>\n<td style=\"width: 286.406px;\"><span id=\"eip-id1167266669989\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_009a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\">Translate into an equation.<\/td>\n<td style=\"width: 286.406px;\"><span id=\"eip-id1167271268957\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_009b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"width: 286.406px;\"><span id=\"eip-id1167271268973\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_009c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\">Subtract 7 from each side and simplify.<\/td>\n<td style=\"width: 286.406px;\"><span id=\"eip-id1167267708487\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_009d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\">Divide each side by 2 and simplify.<\/td>\n<td style=\"width: 286.406px;\"><span id=\"eip-id1167267708501\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_009e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\"><strong>Step 6. Check.<\/strong><\/td>\n<td style=\"width: 286.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\">Is the sum of twice 4 and 7 equal to 15?<\/td>\n<td style=\"width: 286.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-32ad9c985ffce974ef76ae86bfa837a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#43;&#55;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#53;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#53;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"139\" style=\"vertical-align: -15px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 366.406px;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"width: 286.406px;\">The number is 4.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344167538\">Did you notice that we left out some of the steps as we solved this equation? If you\u2019re not yet ready to leave out these steps, write down as many as you need.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344300575\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344294400\" data-type=\"exercise\">\n<div id=\"fs-id1168344294402\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344294402\" data-type=\"problem\">\n<p id=\"fs-id1168344164747\">The sum of four times a number and two is 14. Find the number.<\/p>\n<\/div>\n<div id=\"fs-id1168344227099\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344227102\">3<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344248658\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344294861\" data-type=\"exercise\">\n<div id=\"fs-id1168344294864\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344294864\" data-type=\"problem\">\n<p id=\"fs-id1168344249726\">The sum of three times a number and seven is 25. Find the number.<\/p>\n<\/div>\n<div id=\"fs-id1168344246276\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344246278\">6<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344249797\">Some number word problems ask us to find two or more numbers. It may be tempting to name them all with different variables, but so far we have only solved equations with one variable. In order to avoid using more than one variable, we will define the numbers in terms of the same variable. Be sure to read the problem carefully to discover how all the numbers relate to each other.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344156561\" data-type=\"problem\">\n<p id=\"fs-id1168344248092\">One number is five more than another. The sum of the numbers is 21. Find the numbers.<\/p>\n<\/div>\n<div id=\"fs-id1168344317629\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 50%;\"><strong>Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td style=\"height: 30px; width: 50%;\">We are looking for two numbers.<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 50%;\"><strong>Step 3. Name.<\/strong> We have two numbers to name and need a name for each.<\/td>\n<td style=\"height: 30px; width: 50%;\"><\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"height: 46px; width: 50%;\">Choose a variable to represent the first number.<\/td>\n<td style=\"height: 46px; width: 50%;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-90a3c1a9019e7967d044ff6defb38a6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#123;&#49;&#125;&#94;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#115;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"53\" style=\"vertical-align: -1px;\" \/> number.<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 50%;\">What do we know about the second number?<\/td>\n<td style=\"height: 30px; width: 50%;\">One number is five more than another.<\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"height: 46px; width: 50%;\"><\/td>\n<td style=\"height: 46px; width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5f1d8de64562b3ef14ccdd111492ccc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#53;&#61;&#123;&#50;&#125;&#94;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#110;&#100;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"90\" style=\"vertical-align: -2px;\" \/> number<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 50%;\"><strong>Step 4. Translate. <\/strong>Restate the problem as one sentence with all the important information.<\/td>\n<td style=\"height: 30px; width: 50%;\">The sum of the 1<sup>st<\/sup> number and the 2<sup>nd<\/sup> number is 21.<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px; width: 50%;\">Translate into an equation.<\/td>\n<td style=\"height: 16px; width: 50%;\"><span id=\"eip-id1167270290107\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\">Substitute the variable expressions.<\/td>\n<td style=\"height: 14px; width: 50%;\"><span id=\"eip-id1167261276092\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"height: 14px; width: 50%;\"><span id=\"eip-id1167261210912\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\">Combine like terms.<\/td>\n<td style=\"height: 14px; width: 50%;\"><span id=\"eip-id1167265412776\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\">Subtract 5 from both sides and simplify.<\/td>\n<td style=\"height: 14px; width: 50%;\"><span id=\"eip-id1167270270940\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\">Divide by 2 and simplify.<\/td>\n<td style=\"height: 14px; width: 50%;\"><span id=\"eip-id1167269810887\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\">Find the second number, too.<\/td>\n<td style=\"height: 14px; width: 50%;\"><span id=\"eip-id1167265724617\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\"><\/td>\n<td style=\"height: 14px; width: 50%;\"><span id=\"eip-id1167265755574\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\"><\/td>\n<td style=\"height: 14px; width: 50%;\"><span id=\"eip-id1167263283439\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_010i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\"><strong>Step 6. Check.<\/strong><\/td>\n<td style=\"height: 14px; width: 50%;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\">Do these numbers check in the problem?<\/td>\n<td style=\"height: 14px; width: 50%;\"><\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"height: 46px; width: 50%;\">Is one number 5 more than the other?<\/td>\n<td style=\"width: 50%; height: 46px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ff33373f6fd06d6f047c13bf89a53b86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#54;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#51;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#56;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"79\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 50%;\">Is thirteen 5 more than 8? Yes.<\/td>\n<td style=\"width: 50%; height: 30px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c5096cbb78dfd57c57f06a0deb1cfe8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#54;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#51;&#61;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"59\" style=\"vertical-align: 0px;\" \/>\u2713<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 50%;\">Is the sum of the two numbers 21?<\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7af4b35f05a14e96805be140a3f53219_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#43;&#49;&#51;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"89\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 50%;\"><\/td>\n<td style=\"width: 50%; height: 30px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e35f0d11d4a4c529c4c04daf1df50386_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#54;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#49;&#61;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"59\" style=\"vertical-align: 0px;\" \/>\u2713<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 16px; width: 50%;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"height: 16px; width: 50%;\">The numbers are 8 and 13.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344294396\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344293581\" data-type=\"exercise\">\n<div id=\"fs-id1168344293583\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344293583\" data-type=\"problem\">\n<p id=\"fs-id1168344307620\">One number is six more than another. The sum of the numbers is twenty-four. Find the numbers.<\/p>\n<\/div>\n<div id=\"fs-id1168344307624\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344331833\">9, 15<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344124889\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344319163\" data-type=\"exercise\">\n<div id=\"fs-id1168344319165\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344319165\" data-type=\"problem\">\n<p id=\"fs-id1168344319167\">The sum of two numbers is fifty-eight. One number is four more than the other. Find the numbers.<\/p>\n<\/div>\n<div id=\"fs-id1168344331562\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344124827\">27, 31<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344307236\" data-type=\"problem\">\n<p id=\"fs-id1168344307238\">The sum of two numbers is negative fourteen. One number is four less than the other. Find the numbers.<\/p>\n<\/div>\n<div id=\"fs-id1168344296813\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td style=\"width: 50%;\">We are looking for two numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 3. Name.<\/strong><\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Choose a variable.<\/td>\n<td style=\"width: 50%;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-90a3c1a9019e7967d044ff6defb38a6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#123;&#49;&#125;&#94;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#115;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"53\" style=\"vertical-align: -1px;\" \/> number.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">One number is 4 less than the other.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fa94603e0a43b06f95791570f743ee44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#45;&#52;&#61;&#123;&#50;&#125;&#94;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#110;&#100;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -1px;\" \/> number<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 4. Translate. <\/strong><\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Write as one sentence.<\/td>\n<td style=\"width: 50%;\">The sum of the 2 numbers is negative 14.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Translate into an equation.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271084715\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271346165\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Combine like terms.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271102471\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Add 4 to each side and simplify.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271105692\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167268226870\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167267771016\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167267808396\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167268169938\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"fs-id1169149340877\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_011i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 6. Check.<\/strong><\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Is \u22129 four less than \u22125?<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bc9483154dee0ad22d37debdf48b254b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#53;&#45;&#52;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"103\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aeb2a3264d3287dfd7615efee3bf6e14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#46;&#55;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#57;&#61;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"72\" style=\"vertical-align: 0px;\" \/>\u2713<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Is their sum \u221214?<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40d54e7473a33ab72ec2e9439f7a1367_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"135\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e28932ccdb1de2efdae3461d4cee67fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#46;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#49;&#52;&#61;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"90\" style=\"vertical-align: 0px;\" \/>\u2713<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"width: 50%;\">The numbers are \u22125 and \u22129.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344299552\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344299556\" data-type=\"exercise\">\n<div id=\"fs-id1168344301712\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344301712\" data-type=\"problem\">\n<p id=\"fs-id1168344301714\">The sum of two numbers is negative twenty-three. One number is seven less than the other. Find the numbers.<\/p>\n<\/div>\n<div id=\"fs-id1168344282379\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344282382\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-08a6420a7f2009801f497c63ee38a72e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;&#44;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"61\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344286120\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344247223\" data-type=\"exercise\">\n<div id=\"fs-id1168344247225\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344247225\" data-type=\"problem\">\n<p id=\"fs-id1168344281911\">The sum of two numbers is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb9e52ddecc045b16dbf509b1c89f11b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/>. One number is 40 more than the other. Find the numbers.<\/p>\n<\/div>\n<div id=\"fs-id1168344252714\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344228726\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-562c7a428b60e681465f834e50c30f83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#57;&#44;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344316446\" data-type=\"problem\">\n<p id=\"fs-id1168344316449\">One number is ten more than twice another. Their sum is one. Find the numbers.<\/p>\n<\/div>\n<div id=\"fs-id1168344247697\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\"><strong>Step 2. Identify<\/strong> what you are looking for.<\/td>\n<td style=\"width: 50%; height: 30px;\">We are looking for two numbers.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><strong>Step 3. Name.<\/strong><\/td>\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Choose a variable.<\/td>\n<td style=\"width: 50%; height: 14px;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-93cab3de7b15ae443304b2f5794ded16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#123;&#49;&#125;&#94;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#115;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"53\" style=\"vertical-align: -1px;\" \/> number.<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">One number is 10 more than twice another.<\/td>\n<td style=\"width: 50%; height: 30px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ff4f740f4370215016766500429a63b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#49;&#48;&#61;&#123;&#50;&#125;&#94;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#110;&#100;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"107\" style=\"vertical-align: -2px;\" \/> number<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><strong>Step 4. Translate. <\/strong><\/td>\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Restate as one sentence.<\/td>\n<td style=\"width: 50%; height: 14px;\">Their sum is one.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<td style=\"width: 50%; height: 14px;\">The sum of the two numbers is 1.<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">Translate into an equation.<\/td>\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1167261277458\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_012a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">Combine like terms.<\/td>\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1167263282944\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_012b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">Subtract 10 from each side.<\/td>\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1167263494986\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_012c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">Divide each side by 3.<\/td>\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1167270181053\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_012d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\"><\/td>\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1167265669857\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_012e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\"><\/td>\n<td style=\"width: 50%; height: 15px;\"><span id=\"eip-id1167269925286\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_012f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 50%; height: 18px;\"><\/td>\n<td style=\"width: 50%; height: 18px;\"><span id=\"eip-id1167270172734\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_012g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\"><\/td>\n<td style=\"width: 50%; height: 15px;\"><span id=\"fs-id1169148888999\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_012h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><strong>Step 6. Check.<\/strong><\/td>\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">Is ten more than twice \u22123 equal to 4?<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-80f814fe0b6103af182a8da4853a6ce2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#49;&#48;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"120\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e09b70501b20322872d6e8b8f42bd886_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#54;&#43;&#49;&#48;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"97\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f86434758f2592337489323dbd68ee48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#46;&#56;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/>\u2713<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Is their sum 1?<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-86df18d3de3ce2a8f5eb9edc76971d1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#51;&#43;&#52;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"87\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-05297f5b9b36f0c0060bc1a48cac7f3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#46;&#56;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: 0px;\" \/>\u2713<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"width: 50%; height: 30px;\">The numbers are \u22123 and \u22124.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344254538\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344254541\" data-type=\"exercise\">\n<div id=\"fs-id1168344285604\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344285604\" data-type=\"problem\">\n<p id=\"fs-id1168344285606\">One number is eight more than twice another. Their sum is negative four. Find the numbers.<\/p>\n<\/div>\n<div id=\"fs-id1168344125501\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344125503\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f034bd5276965afe6b6ab91c155288d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#44;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344330486\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344308700\" data-type=\"exercise\">\n<div id=\"fs-id1168344308702\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344308702\" data-type=\"problem\">\n<p id=\"fs-id1168344308704\">One number is three more than three times another. Their sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/>. Find the numbers.<\/p>\n<\/div>\n<div id=\"fs-id1168344298821\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344298823\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3c9cc35d5d29a8759bfde859df472b13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#44;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344319176\">Some number problems involve consecutive integers.<em data-effect=\"italics\">Consecutive integers<\/em> are integers that immediately follow each other.<\/p>\n<p>\u00a0Examples of consecutive integers are:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-41a6bba6a02972d90ab82c0e349c79b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#49;&#44;&#50;&#44;&#51;&#44;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#45;&#49;&#48;&#44;&#45;&#57;&#44;&#45;&#56;&#44;&#45;&#55;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#49;&#53;&#48;&#44;&#49;&#53;&#49;&#44;&#49;&#53;&#50;&#44;&#49;&#53;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"82\" width=\"130\" style=\"vertical-align: -37px;\" \/><\/p>\n<p id=\"fs-id1168344327961\">Notice that each number is one more than the number preceding it. So if we define the first integer as <em data-effect=\"italics\">n<\/em>, the next consecutive integer is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d72f4e3699652cfc70b8880515893d7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -2px;\" \/>. The one after that is one more than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d72f4e3699652cfc70b8880515893d7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -2px;\" \/>, so it is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a49e214171dd9ed306bb9dc52c01d658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#49;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"71\" style=\"vertical-align: -2px;\" \/>, which is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-47d55edfa96136aa77a4cb02acfcb034_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ba6cf1613a9128d074731d673d619511_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#49;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#116;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#43;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#50;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#43;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#51;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#32;&#46;&#32;&#46;&#32;&#46;&#32;&#101;&#116;&#99;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"334\" style=\"vertical-align: -25px;\" \/><\/p>\n<div id=\"fs-id1168344249461\" class=\"bc-section section\" data-depth=\"1\">\n<div data-type=\"equation\" data-label=\"\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344296047\" data-type=\"problem\">\n<p id=\"fs-id1168344296049\">The sum of two consecutive integers is 47. Find the numbers.<\/p>\n<\/div>\n<div id=\"fs-id1168344296053\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 2. Identify<\/strong> what you are looking for.<\/td>\n<td style=\"width: 50%;\">two consecutive integers<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 3. Name<\/strong> each number.<\/td>\n<td style=\"width: 50%;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-90a3c1a9019e7967d044ff6defb38a6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#123;&#49;&#125;&#94;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#115;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"53\" style=\"vertical-align: -1px;\" \/> integer.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cb2e09187187f6d82f16d715b9982411_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#49;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"59\" style=\"vertical-align: -2px;\" \/> next consecutive integer<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 4. Translate. <\/strong><\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Restate as one sentence.<\/td>\n<td style=\"width: 50%;\">The sum of the integers is 47.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Translate into an equation.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167270257414\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_013a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167270256828\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_013b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Combine like terms.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167269983541\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_013c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Subtract 1 from each side.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167261209602\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_013d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Divide each side by 2.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167270290555\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_013e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167263494184\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_013f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167269975642\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_013g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167269972879\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_013h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 6. Check.<\/strong><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b9fe3434159247816d170332645605c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#51;&#43;&#50;&#52;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#52;&#55;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#55;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#52;&#55;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"135\" style=\"vertical-align: -15px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"width: 50%;\">The two consecutive integers are 23 and 24.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344281852\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344308176\" data-type=\"exercise\">\n<div id=\"fs-id1168344308178\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344308178\" data-type=\"problem\">\n<p id=\"fs-id1168344308180\">The sum of two consecutive integers is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ffb4dcee510557d85b10c85d699e726c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/>. Find the numbers.<\/p>\n<\/div>\n<div id=\"fs-id1168344281649\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344281651\">47, 48<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344281658\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344281661\" data-type=\"exercise\">\n<div id=\"fs-id1168344281663\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344281663\" data-type=\"problem\">\n<p id=\"fs-id1168344281665\">The sum of two consecutive integers is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aef29fb3b7f163a804596c378eba113f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/>. Find the numbers.<\/p>\n<\/div>\n<div id=\"fs-id1168344250051\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344250053\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-78cd2a516e78aa1651b765049dc5ee45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;&#44;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"69\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344286019\" data-type=\"problem\">\n<p id=\"fs-id1168344286021\">Find three consecutive integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc9ede649c07c07c0c778c8ce8270b42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168344286032\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td style=\"width: 50%;\">three consecutive integers<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 3. Name<\/strong> each of the three numbers.<\/td>\n<td style=\"width: 50%;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-90a3c1a9019e7967d044ff6defb38a6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#123;&#49;&#125;&#94;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#115;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"53\" style=\"vertical-align: -1px;\" \/> integer.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cb2e09187187f6d82f16d715b9982411_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#49;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"59\" style=\"vertical-align: -2px;\" \/> 2<sup>nd<\/sup> consecutive integer<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3fceb0270375ebb50f16deb96ae98485_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#50;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"59\" style=\"vertical-align: -2px;\" \/> 3<sup>rd<\/sup> consecutive integer<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 4. Translate. <\/strong><\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Restate as one sentence.<\/td>\n<td style=\"width: 50%;\">The sum of the three integers is \u221242.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Translate into an equation.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167268280403\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167266954802\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Combine like terms.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167266954810\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Subtract 3 from each side.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271093107\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Divide each side by 3.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271070796\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271016239\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271181140\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167270951708\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271234318\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167270916307\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167267549035\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_014k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 6. Check.<\/strong><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fca26c2106a1ef10cd9323c4895fc446_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#49;&#51;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#52;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#52;&#50;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#52;&#50;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"257\" style=\"vertical-align: -15px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"width: 50%;\">The three consecutive integers are \u221213, \u221214, and \u221215.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344319103\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344319106\" data-type=\"exercise\">\n<div id=\"fs-id1168344319108\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344319108\" data-type=\"problem\">\n<p id=\"fs-id1168344278804\">Find three consecutive integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-68ec54e7d36d1f7bd013e83bd1b9e129_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344278816\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc7dd560e2c776aa26b7a15ca8599dc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#51;&#44;&#45;&#51;&#50;&#44;&#45;&#51;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344297618\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344297621\" data-type=\"exercise\">\n<div id=\"fs-id1168344297624\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344297624\" data-type=\"problem\">\n<p id=\"fs-id1168344297626\">Find three consecutive integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3d317efb244f5cda02f971b5e4865cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168344297636\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344297638\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-28662bf55d27b9f72d89bcc54ae6b82c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#51;&#44;&#45;&#49;&#50;&#44;&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344249061\">Now that we have worked with consecutive integers, we will expand our work to include consecutive even integers and consecutive odd integers. <em data-effect=\"italics\">Consecutive even integers<\/em> are even integers that immediately follow one another. Examples of consecutive even integers are:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b721883795b94ba03572aad823e6c401_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#49;&#56;&#44;&#50;&#48;&#44;&#50;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#54;&#52;&#44;&#54;&#54;&#44;&#54;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#45;&#49;&#50;&#44;&#45;&#49;&#48;&#44;&#45;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"82\" width=\"102\" style=\"vertical-align: -37px;\" \/><\/p>\n<p id=\"fs-id1168344246163\">Notice each integer is 2 more than the number preceding it. If we call the first one <em data-effect=\"italics\">n<\/em>, then the next one is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-47d55edfa96136aa77a4cb02acfcb034_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -2px;\" \/>. The next one would be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70d627a93bcc7ae846b0a30b572670a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#50;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"71\" style=\"vertical-align: -2px;\" \/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b9896c061b5efc493613885b3e023fa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"41\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-881a2b79c828b4848f5d2a66bbdf0891_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#49;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#116;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#101;&#118;&#101;&#110;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#43;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#50;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#101;&#118;&#101;&#110;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#43;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#51;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#101;&#118;&#101;&#110;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#32;&#46;&#32;&#46;&#32;&#46;&#32;&#101;&#116;&#99;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"374\" style=\"vertical-align: -25px;\" \/><\/p>\n<p id=\"fs-id1168344302427\"><em data-effect=\"italics\">Consecutive odd integers<\/em> are odd integers that immediately follow one another. Consider the consecutive odd integers 77, 79, and 81<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9f9c25ac14da307c084504b8fbbe06dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#55;&#55;&#44;&#55;&#57;&#44;&#56;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#110;&#44;&#110;&#43;&#50;&#44;&#110;&#43;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"109\" style=\"vertical-align: -26px;\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3ffee27e3b4cee8626c6fabeb6a5f562_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#49;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#116;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#100;&#100;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#43;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#50;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#111;&#100;&#100;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#43;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#51;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#111;&#100;&#100;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#32;&#46;&#32;&#46;&#32;&#46;&#32;&#101;&#116;&#99;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"369\" style=\"vertical-align: -25px;\" \/><\/p>\n<p id=\"fs-id1168344306541\">Does it seem strange to add 2 (an even number) to get from one odd integer to the next? Do you get an odd number or an even number when we add 2 to 3? to 11? to 47?<\/p>\n<p id=\"fs-id1168344306546\">Whether the problem asks for consecutive even numbers or odd numbers, you don\u2019t have to do anything different. The pattern is still the same\u2014to get from one odd or one even integer to the next, add 2<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344306557\" data-type=\"problem\">\n<p id=\"fs-id1168344306560\">Find three consecutive even integers whose sum is 84<\/p>\n<\/div>\n<div id=\"fs-id1168344306564\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-57\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td style=\"width: 204.406px;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"width: 448.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\"><strong>Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td style=\"width: 448.406px;\">three consecutive even integers<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\"><strong>Step 3. Name<\/strong> the integers.<\/td>\n<td style=\"width: 448.406px;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b734576de3bec67d4cc5191e0e847674_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#123;&#49;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"53\" style=\"vertical-align: -1px;\" \/> even integer.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7ab633254270961de8544086719c9535_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#50;&#61;&#123;&#50;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#100;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"90\" style=\"vertical-align: -2px;\" \/> consecutive even integer<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0872ff82125aca7a245af6ff2f9e5b05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#52;&#61;&#123;&#51;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#100;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"87\" style=\"vertical-align: -2px;\" \/> consecutive even integer<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\"><strong>Step 4. Translate.<\/strong><\/td>\n<td style=\"width: 448.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\">Restate as one sentence.<\/td>\n<td style=\"width: 448.406px;\">The sume of the three even integers is 84.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\">Translate into an equation.<\/td>\n<td style=\"width: 448.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-115bcb596d659782c6a92d75098ab3ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#110;&#43;&#50;&#43;&#110;&#43;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#61;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#56;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"185\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"width: 448.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\">Combine like terms.<\/td>\n<td style=\"width: 448.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-115bcb596d659782c6a92d75098ab3ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#110;&#43;&#50;&#43;&#110;&#43;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#61;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#56;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"185\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\">Subtract 6 from each side.<\/td>\n<td style=\"width: 448.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5f396f601ebbf415656945c21ef5e56b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#110;&#43;&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#61;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#56;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"99\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\">Divide each side by 3.<\/td>\n<td style=\"width: 448.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-15ad38adbef71545c984c69a3aefe796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#110;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#61;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#55;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"68\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\"><\/td>\n<td style=\"width: 448.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2f1227b040c4084dfdaf3ad90e31030e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#125;&#110;&#61;&#50;&#54;&#38;&#32;&#123;&#49;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#116;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#92;&#32;&#92;&#92;&#32;&#110;&#43;&#50;&#38;&#32;&#123;&#50;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#92;&#32;&#50;&#54;&#43;&#50;&#38;&#32;&#92;&#92;&#32;&#50;&#56;&#38;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#110;&#43;&#52;&#38;&#32;&#123;&#51;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#92;&#32;&#50;&#54;&#43;&#52;&#38;&#32;&#92;&#92;&#32;&#51;&#48;&#38;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"192\" width=\"150\" style=\"vertical-align: -88px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\"><strong>Step 6. Check.<\/strong><\/td>\n<td style=\"width: 448.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9732784618cba6e164cdebec84dd2447_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#50;&#54;&#43;&#50;&#56;&#43;&#51;&#48;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#56;&#52;&#92;&#92;&#32;&#56;&#52;&#61;&#56;&#52;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"138\" style=\"vertical-align: -15px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204.406px;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"width: 448.406px;\">The three consecutive integers are 26, 28, and 30.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344334628\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344334632\" data-type=\"exercise\">\n<div id=\"fs-id1168344334634\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344334634\" data-type=\"problem\">\n<p id=\"fs-id1168344334636\">Find three consecutive even integers whose sum is 102<\/p>\n<\/div>\n<div id=\"fs-id1168344334640\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344334643\">32, 34, 36<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344297579\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344297582\" data-type=\"exercise\">\n<div id=\"fs-id1168344297584\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344297584\" data-type=\"problem\">\n<p id=\"fs-id1168344297586\">Find three consecutive even integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d15aa1d60ab00024197b84d5e3e3d75e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168344297597\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344297599\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b696c1489b3ae94ea305a5549d03332_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#44;&#45;&#56;&#44;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"92\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344126231\" data-type=\"problem\">\n<p id=\"fs-id1168344126233\">A married couple together earns &#36;110,000 a year. The wife earns &#36;16,000 less than twice what her husband earns. What does the husband earn?<\/p>\n<\/div>\n<div id=\"fs-id1168344126239\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 1. Read<\/strong> the problem.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td style=\"width: 50%;\">How much does the husband earn?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 3. Name<\/strong>.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Choose a variable to represent the amount<br \/>\nthe husband earns.<\/td>\n<td style=\"width: 50%;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-62bcd55cff5bacf6b29f3badcbd52342_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"28\" style=\"vertical-align: 0px;\" \/> the amount the husband earns.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">The wife earns &#36;16,000 less than twice that.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3ee865481fec4f444f76dabba0135e3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#104;&#45;&#49;&#54;&#44;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"93\" style=\"vertical-align: -4px;\" \/> the amount the wife earns.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 4. Translate. <\/strong><\/td>\n<td style=\"width: 50%;\">Together the husband and wife earn &#36;110,000.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Restate the problem in one sentence with<br \/>\nall the important information.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271070928\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_015a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Translate into an equation.<\/td>\n<td style=\"width: 50%;\"><span id=\"eip-id1167271070945\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_03_01_015b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 5. Solve<\/strong> the equation.<\/td>\n<td style=\"width: 50%;\">h + 2h \u2212 16,000 = 110,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Combine like terms.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7d5ca1417c1772b25aeb1033fff2f681_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/>3h \u2212 16,000 = 110,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Add 16,000 to both sides and simplify.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1fe9885f484724d99d7185e00b1aa004_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#46;&#55;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/>3h = 126,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Divide each side by 3.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-07d370fdd39b522d6f2b5406082f3169_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#53;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/>h = 42,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2f85f72be64e54839f5c741dbe089a62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#54;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/>&#36;42,000\u2003amount husband earns<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1fe9885f484724d99d7185e00b1aa004_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#46;&#55;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/>2h \u2212 16,000\u2003amount wife earns<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-85d2bba28b4568baf68509ed794fb4a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#56;&#56;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/>2(42,000) \u2212 16,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0a99c72df2eb456d14ff98dc66ebef70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#46;&#48;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/>84,000 \u2212 16,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2f9ac9b83b2b3c09e7ce0fbd4df00d93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#54;&#46;&#56;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/>68,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 6. Check.<\/strong><\/td>\n<td style=\"width: 50%;\">If the wife earns &#36;68,000 and the husband earns &#36;42,000 is the total &#36;110,000? Yes!<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><strong>Step 7. Answer<\/strong> the question.<\/td>\n<td style=\"width: 50%;\">The husband earns &#36;42,000 a year.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344126257\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344332527\" data-type=\"exercise\">\n<div id=\"fs-id1168344332530\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344332530\" data-type=\"problem\">\n<p id=\"fs-id1168344332532\">According to the National Automobile Dealers Association, the average cost of a car in 2014 was 28,500. This was 1,500 less than 6 times the cost in 1975. What was the average cost of a car in 1975?<\/p>\n<\/div>\n<div id=\"fs-id1168344332538\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344332540\">5,000<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344332546\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344338480\" data-type=\"exercise\">\n<div id=\"fs-id1168344338483\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344338483\" data-type=\"problem\">\n<p id=\"fs-id1168344338485\">The Canadian Real Estate Association (CREA) data shows that the median price of new home in the Canada in December 2018 was &#36;470,000. This was &#36;14,000 more than 19 times the price in December 1967. What was the median price of a new home in December 1967?<\/p>\n<\/div>\n<div id=\"fs-id1168344338491\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344338493\">&#36;24,000<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"fs-id1171791390945\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Problem-Solving Strategy<\/strong>\n<ol id=\"fs-id1167265385253\" class=\"stepwise\" type=\"1\">\n<li><strong data-effect=\"bold\">Read<\/strong> the problem. Make sure all the words and ideas are understood.<\/li>\n<li><strong data-effect=\"bold\">Identify<\/strong> what we are looking for.<\/li>\n<li><strong data-effect=\"bold\">Name<\/strong> what we are looking for. Choose a variable to represent that quantity.<\/li>\n<li><strong data-effect=\"bold\">Translate<\/strong> into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.<\/li>\n<li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li>\n<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\n<li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Consecutive Integers<\/strong><br \/>\nConsecutive integers are integers that immediately follow each other.<\/p>\n<div id=\"fs-id1168345325923\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2da39e73cb8d0c127432ee27b716edae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#49;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#116;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#43;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#50;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#32;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#43;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#51;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#32;&#46;&#32;&#46;&#32;&#46;&#32;&#101;&#116;&#99;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"334\" style=\"vertical-align: -25px;\" \/><\/div>\n<p>Consecutive even integers are even integers that immediately follow one another.<\/p>\n<div id=\"fs-id1168345397558\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-077a3ce686d3c4b858221a7a031413a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#49;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#116;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#43;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#50;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#32;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#43;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#51;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#32;&#46;&#32;&#46;&#32;&#46;&#32;&#101;&#116;&#99;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"334\" style=\"vertical-align: -25px;\" \/><\/div>\n<p>Consecutive odd integers are odd integers that immediately follow one another.<\/p>\n<div id=\"fs-id1168341958730\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-077a3ce686d3c4b858221a7a031413a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#49;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#116;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#43;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#50;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#32;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#110;&#43;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#51;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#32;&#46;&#32;&#46;&#32;&#46;&#32;&#101;&#116;&#99;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"334\" style=\"vertical-align: -25px;\" \/><\/div>\n<\/li>\n<\/ul>\n<h1 data-type=\"title\">Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1168344285166\">Use the Approach Word Problems with a Positive Attitude<\/h2>\n<p id=\"fs-id1166424888146\">In the following exercises, prepare the lists described.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 156px;\">\n<tbody>\n<tr style=\"height: 62px;\">\n<td style=\"width: 50%; height: 62px;\">1. List five positive thoughts you can say to yourself that will help you approach word problems with a positive attitude. You may want to copy them on a sheet of paper and put it in the front of your notebook, where you can read them often.<\/td>\n<td style=\"width: 50%; height: 62px;\">2. List five negative thoughts that you have said to yourself in the past that will hinder your progress on word problems. You may want to write each one on a small piece of paper and rip it up to symbolically destroy the negative thoughts.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1168344337083\">Use a Problem-Solving Strategy for Word Problems<\/h2>\n<p id=\"fs-id1166424884530\">In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">3. Two-thirds of the children in the fourth-grade class are girls. If there are 20 girls, what is the total number of children in the class?<\/td>\n<td style=\"width: 50%;\">4. Three-fifths of the members of the school choir are women. If there are 24 women, what is the total number of choir members?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">5. Zachary has 25 country music CDs, which is one-fifth of his CD collection. How many CDs does Zachary have?<\/td>\n<td style=\"width: 50%;\">6. One-fourth of the candies in a bag of M&amp;M\u2019s are red. If there are 23 red candies, how many candies are in the bag?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">7. There are 16 girls in a school club. The number of girls is four more than twice the number of boys. Find the number of boys.<\/td>\n<td style=\"width: 50%;\">8. There are 18 Cub Scouts in Pack 645. The number of scouts is three more than five times the number of adult leaders. Find the number of adult leaders.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">9. Huong is organizing paperback and hardback books for her club\u2019s used book sale. The number of paperbacks is 12 less than three times the number of hardbacks. Huong had 162 paperbacks. How many hardback books were there?<\/td>\n<td style=\"width: 50%;\">10. Jeff is lining up children\u2019s and adult bicycles at the bike shop where he works. The number of children\u2019s bicycles is nine less than three times the number of adult bicycles. There are 42 adult bicycles. How many children\u2019s bicycles are there?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">11. Philip pays &#36;1,620 in rent every month. This amount is &#36;120 more than twice what his brother Paul pays for rent. How much does Paul pay for rent?<\/td>\n<td style=\"width: 50%;\">12. Marc just bought an SUV for &#36;54,000. This is &#36;7,400 less than twice what his wife paid for her car last year. How much did his wife pay for her car?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">13. Laurie has &#36;46,000 invested in stocks and bonds. The amount invested in stocks is &#36;8,000 less than three times the amount invested in bonds. How much does Laurie have invested in bonds?<\/td>\n<td style=\"width: 50%;\">14. Erica earned a total of &#36;50,450 last year from her two jobs. The amount she earned from her job at the store was &#36;1,250 more than three times the amount she earned from her job at the college. How much did she earn from her job at the college?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1168344292961\">Solve Number Problems<\/h2>\n<p id=\"fs-id1166425001516\">In the following exercises, solve each number word problem.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">15. The sum of a number and eight is 12. Find the number.<\/td>\n<td style=\"width: 50%;\">16. The sum of a number and nine is 17. Find the number.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">17. The difference of a number and 12 is three. Find the number.<\/td>\n<td style=\"width: 50%;\">18. The difference of a number and eight is four. Find the number.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">19. The sum of three times a number and eight is 23. Find the number.<\/td>\n<td style=\"width: 50%;\">20. The sum of twice a number and six is 14. Find the number.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">21.The difference of twice a number and seven is 17. Find the number.<\/td>\n<td style=\"width: 50%;\">22. The difference of four times a number and seven is 21. Find the number.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">23. Three times the sum of a number and nine is 12. Find the number.<\/td>\n<td style=\"width: 50%;\">24. Six times the sum of a number and eight is 30. Find the number.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">25. One number is six more than the other. Their sum is 42. Find the numbers.<\/td>\n<td style=\"width: 50%;\">26. One number is five more than the other. Their sum is 33. Find the numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">27. The sum of two numbers is 20. One number is four less than the other. Find the numbers.<\/td>\n<td style=\"width: 50%;\">28. The sum of two numbers is 27. One number is seven less than the other. Find the numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">29. The sum of two numbers is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5efc88a25eac99bdddb5f279a9640b88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"30\" style=\"vertical-align: -1px;\" \/>. One number is nine more than the other. Find the numbers.<\/td>\n<td style=\"width: 50%;\">30. The sum of two numbers is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e04e4698afac1925c1fb3437f5973900_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/>. One number is 35 more than the other. Find the numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">31. The sum of two numbers is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-892c793fd5ef5483a25cc1964620ed07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: 0px;\" \/>. One number is 94 less than the other. Find the numbers.<\/td>\n<td style=\"width: 50%;\">32. The sum of two numbers is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-56aa87b18d09fffd91e0c35c099baeb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#56;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: 0px;\" \/>. One number is 62 less than the other. Find the numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">33. One number is 14 less than another. If their sum is increased by seven, the result is 85. Find the numbers.<\/td>\n<td style=\"width: 50%;\">34. One number is 11 less than another. If their sum is increased by eight, the result is 71. Find the numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">35. One number is five more than another. If their sum is increased by nine, the result is 60. Find the numbers.<\/td>\n<td style=\"width: 50%;\">36. One number is eight more than another. If their sum is increased by 17, the result is 95. Find the numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">37. One number is one more than twice another. Their sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/>. Find the numbers.<\/td>\n<td style=\"width: 50%;\">38. One number is six more than five times another. Their sum is six. Find the numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">39. The sum of two numbers is 14. One number is two less than three times the other. Find the numbers.<\/td>\n<td style=\"width: 50%;\">40. The sum of two numbers is zero. One number is nine less than twice the other. Find the numbers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">41. The sum of two consecutive integers is 77. Find the integers.<\/td>\n<td style=\"width: 50%;\">42. The sum of two consecutive integers is 89. Find the integers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">43. The sum of two consecutive integers is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dd97a36455222fbbcd36f22967b75707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/>. Find the integers.<\/td>\n<td style=\"width: 50%;\">44. The sum of two consecutive integers is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a59867b5a3525d9c7f91084fbd12ef9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/>. Find the integers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">45. The sum of three consecutive integers is 78. Find the integers.<\/td>\n<td style=\"width: 50%;\">46. The sum of three consecutive integers is 60. Find the integers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">47. Find three consecutive integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3d317efb244f5cda02f971b5e4865cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 50%;\">48. Find three consecutive integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">49. Find three consecutive even integers whose sum is 258.<\/td>\n<td style=\"width: 50%;\">50. Find three consecutive even integers whose sum is 222.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">51. Find three consecutive odd integers whose sum is 171.<\/td>\n<td style=\"width: 50%;\">52. Find three consecutive odd integers whose sum is 291.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">53. Find three consecutive even integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3d317efb244f5cda02f971b5e4865cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 50%;\">54. Find three consecutive even integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1ca0b09b1d64b0c44f550249d0ab3ddf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">55. Find three consecutive odd integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7bcbb08d1f9c7c996216187d4249e664_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 50%;\">56. Find three consecutive odd integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-48b93e93ea7a885efb31bae854ee34cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#54;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3 data-type=\"title\">Everyday Math<\/h3>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">57.<strong data-effect=\"bold\"> Sale Price.<\/strong> Patty paid &#36;35 for a purse on sale for &#36;10 off the original price. What was the original price of the purse?<\/td>\n<td style=\"width: 50%;\">58.<strong data-effect=\"bold\"> Sale Price.<\/strong> Travis bought a pair of boots on sale for &#36;25 off the original price. He paid &#36;60 for the boots. What was the original price of the boots?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">59.<strong data-effect=\"bold\"> Buying in Bulk.<\/strong> Minh spent &#36;6.25 on five sticker books to give his nephews. Find the cost of each sticker book.<\/td>\n<td style=\"width: 50%;\">60.<strong data-effect=\"bold\"> Buying in Bulk.<\/strong> Alicia bought a package of eight peaches for &#36;3.20. Find the cost of each peach.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">61.<strong data-effect=\"bold\"> Price before Sales Tax.<\/strong> Tom paid &#36;1,166.40 for a new refrigerator, including &#36;86.40 tax. What was the price of the refrigerator?<\/td>\n<td style=\"width: 50%;\">62.<strong data-effect=\"bold\"> Price before Sales Tax.<\/strong> Kenji paid &#36;2,279 for a new living room set, including &#36;129 tax. What was the price of the living room set?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3 data-type=\"title\">Writing Exercises<\/h3>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">63. What has been your past experience solving word problems?<\/td>\n<td style=\"width: 50%;\">64. When you start to solve a word problem, how do you decide what to let the variable represent?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">65. What are consecutive odd integers? Name three consecutive odd integers between 50 and 60.<\/td>\n<td style=\"width: 50%;\">66. What are consecutive even integers? Name three consecutive even integers between <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-862746467ef7a474e7ee68e5f343ac7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e9e8668f98ca5c439e8df86b7e3360a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 192px;\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">1. Answers will vary<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">3. 30<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">5. 125<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">7. 6<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">9. 58<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">11. &#36;750<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">13. &#36;13,500<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">15. 4<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">17. 15<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">19. 5<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">21. 12<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">25. 18, 24<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">27. 8, 12<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-65a75cdca75d024a19338fa6f26afe35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#56;&#44;&#45;&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"70\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1ae99ea556b45dc53560a96f290a5018_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#49;&#44;&#45;&#50;&#48;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">33. 32, 46<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">35. 23, 28<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c7b4bffb0147a461feb0eb3fde6a2228_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#44;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"53\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">39. 4, 10<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">41. 38, 39<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9508221ab64d18773d6ea3894d979d37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#44;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"69\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">45. 25, 26, 27<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-78979a60c1272f7a604af5fe7a1a5abf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#44;&#45;&#49;&#50;&#44;&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">49. 84, 86, 88<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">51. 55, 57, 59<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-12613bd9b3392163f5c61bd44ebff781_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#44;&#45;&#49;&#50;&#44;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b46cade56ae903904bd872fda1b0ca7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#57;&#44;&#45;&#55;&#49;&#44;&#45;&#55;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">57. &#36;45<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">59. &#36;1.25<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">61. &#36;1080<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">63. Answers will vary<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">65. Consecutive odd integers are odd numbers that immediately follow each other. An example of three consecutive odd integers between 50 and 60 would be 51, 53, and 55.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cUse a Problem-Solving Strategy\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n","protected":false},"author":90,"menu_order":8,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1365","chapter","type-chapter","status-publish","hentry"],"part":767,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1365","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1365\/revisions"}],"predecessor-version":[{"id":1366,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1365\/revisions\/1366"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/767"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1365\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=1365"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1365"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=1365"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=1365"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}