{"id":1669,"date":"2021-06-04T16:26:45","date_gmt":"2021-06-04T16:26:45","guid":{"rendered":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/applications\/"},"modified":"2021-08-31T21:32:29","modified_gmt":"2021-08-31T21:32:29","slug":"applications","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/applications\/","title":{"raw":"6.3 Proportions; Health Applications","rendered":"6.3 Proportions; Health Applications"},"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 it is expected that you will be able to:\n<ul>\n \t<li>Use the definition of proportion<\/li>\n \t<li>Solve proportions<\/li>\n \t<li>Solve applications using proportions<\/li>\n \t<li>Write percent equations as proportions<\/li>\n \t<li>Translate and solve percent proportions<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Use the Definition of Proportion<\/h1>\n<p id=\"fs-id1682902\">When two ratios or rates are equal, the equation relating them is called a proportion.<\/p>\n\n<div id=\"fs-id1878909\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Proportion<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1166492018126\">A proportion is an equation of the form \\(\\frac{a}{b}=\\frac{c}{d}\\), where \\(b\\ne 0,d\\ne 0\\).<\/p>\n<p id=\"fs-id1166490779333\">The proportion states two ratios or rates are equal. The proportion is read \\(\\text{\u201c}a\\) is to \\(b\\), as \\(c\\) is to \\(d\\text{\u201d.}\\)<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166497354347\">The equation \\(\\frac{1}{2}=\\frac{4}{8}\\) is a proportion because the two fractions are equal. The proportion \\(\\frac{1}{2}=\\frac{4}{8}\\) is read \\(\\text{\u201c}1\\) is to \\(2\\) as \\(4\\) is to \\(8\\text{\u201d.}\\)<\/p>\n<p id=\"fs-id1166492788523\">If we compare quantities with units, we have to be sure we are comparing them in the right order.<\/p>\n\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-id1166494585692\" data-type=\"problem\">\n<p id=\"fs-id1287243\">Write the sentence as a proportion:<\/p>\n72 heartbeats in 1 minute is the same as 216 heartbeats in 3 minutes.\n\n<\/div>\n<div id=\"fs-id1166482132364\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468496922\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 39.2523%;\"><\/td>\n<td style=\"width: 60.7477%;\">72 is to 1 as 216 is to 3.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 39.2523%;\">Write as a proportion.<\/td>\n<td style=\"width: 60.7477%;\">\u00a0\\(\\frac{\\text{72 heartbeats}}\u00a0 {\\text{1 minute}}=\\frac{\\text{216 heartbeats}}{\\text{3 minutes}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1166492788601\">Write the sentence as a proportion:<\/p>\n\\(\\phantom{\\rule{0.2em}{0ex}}5\\) is to \\(9\\) as \\(20\\) is to \\(36\\).\n\n<\/div>\n<details><summary>Show answer<\/summary>\n<div id=\"fs-id1956784\" data-type=\"solution\">\n\n\\(\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{9}=\\frac{20}{36}\\phantom{\\rule{0.2em}{0ex}}\\)\n\n<\/div>\n<\/details><\/div>\n<\/div>\n<p id=\"fs-id1097912\">Look at the proportions \\(\\frac{1}{2}=\\frac{4}{8}\\) and \\(\\frac{2}{3}=\\frac{6}{9}\\). From our work with equivalent fractions we know these equations are true. But how do we know if an equation is a proportion with equivalent fractions if it contains fractions with larger numbers?<\/p>\n<p id=\"fs-id1166498443767\">To determine if a proportion is true, we find the <strong data-effect=\"bold\">cross products<\/strong> of each proportion. To find the cross products, we multiply each denominator with the opposite numerator (diagonally across the equal sign). The results are called a cross products because of the cross formed. The cross products of a proportion are equal.<\/p>\n<span id=\"fs-id1731746\" data-type=\"media\" data-alt=\"The figure shows cross multiplication of two proportions. There is the proportion 1 is to 2 as 4 is to 8. Arrows are shown diagonally across the equal sign to show cross products. The equations formed by cross multiplying are 8 \u00b7 1 = 8 and 2 \u00b7 4 = 8. There is the proportion 2 is to 3 as 6 is to 9. Arrows are shown diagonally across the equal sign to show cross products. The equations formed by cross multiplying are 9 \u00b7 2 = 18 and 3 \u00b7 6 = 18.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_028_img.jpg\" alt=\"The figure shows cross multiplication of two proportions. There is the proportion 1 is to 2 as 4 is to 8. Arrows are shown diagonally across the equal sign to show cross products. The equations formed by cross multiplying are 8 \u00b7 1 = 8 and 2 \u00b7 4 = 8. There is the proportion 2 is to 3 as 6 is to 9. Arrows are shown diagonally across the equal sign to show cross products. The equations formed by cross multiplying are 9 \u00b7 2 = 18 and 3 \u00b7 6 = 18.\" data-media-type=\"image\/jpeg\"><\/span>\n<div id=\"fs-id1166489098476\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Cross Products of a Proportion<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1517408\">For any proportion of the form \\(\\frac{a}{b}=\\frac{c}{d}\\), where \\(b\\ne 0,d\\ne 0\\), its cross products are equal.<\/p>\n<span id=\"fs-id1166494770801\" data-type=\"media\" data-alt=\"No Alt Text\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_003_img.jpg\" alt=\"No Alt Text\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1501697\">Cross products can be used to test whether a proportion is true. To test whether an equation makes a proportion, we find the cross products. If they are the equal, we have a proportion.<\/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-id1476424\" data-type=\"problem\">\n<p id=\"fs-id1166497362535\">Determine whether each equation is a proportion:<\/p>\n\n<ol id=\"eip-id1168466230295\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{9}=\\frac{12}{28}\\)<\/li>\n \t<li>\\(\\frac{17.5}{37.5}=\\frac{7}{15}\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1946221\" data-type=\"solution\">\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1491625\">To determine if the equation is a proportion, we find the cross products. If they are equal, the equation is a proportion.<\/p>\n\n<table id=\"eip-id1168468703669\" style=\"width: 100%;\" summary=\"The figure shows the steps to finding the cross products of the proportion 4 is to 9 as 12 is to 28. The cross multiplication shown is 28 times 4 = 112 and 9 times 12 = 28.\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467196647\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_020_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Find the cross products.<\/td>\n<td>\\(28\\cdot 4=112\\phantom{\\rule{2em}{0ex}}9\\cdot 12=108\\)\n\n<span data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_020_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166481190972\">Since the cross products are not equal, \\(28\\cdot4\\ne 9\\cdot12\\), the equation is not a proportion.<\/p>\n\n<table id=\"eip-id1168469699712\" style=\"width: 100%;\" summary=\"The figure shows the steps to finding the cross products of the proportion 17.5 is to 37.5 as 7 is to 15. The cross multiplication shown is 15 times 17.5 = 262.5 and 37.5 times 7 = 262.5.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 28.6363%;\">b)<\/td>\n<td style=\"width: 71.25%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 28.6363%;\"><\/td>\n<td style=\"width: 71.25%;\"><span id=\"eip-id1168469613430\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_021_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 28.6363%;\">Find the cross products.<\/td>\n<td style=\"width: 71.25%;\">\\(15\\cdot 17.5=262.5\\phantom{\\rule{2em}{0ex}}37.5\\cdot 7=262.5\\)\n\n<span id=\"eip-id1168466166406\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_021_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1956342\">Since the cross products are equal, \\(15\\cdot17.5=37.5\\cdot7\\), the equation is a proportion.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1431411\" data-type=\"problem\">\n<p id=\"fs-id1359170\">Determine whether each equation is a proportion:<\/p>\n\n<ol id=\"eip-id1168468436941\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{9}=\\frac{54}{72}\\)<\/li>\n \t<li>\\(\\frac{24.5}{45.5}=\\frac{7}{13}\\)<\/li>\n<\/ol>\n<\/div>\n<details><summary>Show answer<\/summary>\n<div id=\"fs-id1166482688691\" data-type=\"solution\">\n<ol id=\"eip-id1168468413917\" class=\"circled\" type=\"a\">\n \t<li>no<\/li>\n \t<li>yes<\/li>\n<\/ol>\n<\/div>\n<\/details><\/div>\n<\/div>\n<h1>Solve Proportions<\/h1>\n<p id=\"fs-id1166491085133\">To solve a proportion containing a variable, we remember that the proportion is an equation. All of the techniques we have used so far to solve equations still apply. In the next example, we will solve a proportion by multiplying by the <span class=\"no-emphasis\" data-type=\"term\">Least Common Denominator<\/span> (LCD) using the <span class=\"no-emphasis\" data-type=\"term\">Multiplication Property of Equality<\/span>.<\/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-id1944367\" data-type=\"problem\">\n<p id=\"fs-id1166494756631\">Solve: \\(\\frac{x}{63}=\\frac{4}{7}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1626522\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468652606\" style=\"width: 100%;\" summary=\"The figure shows the steps to finding the cross products of the proportion 17.5 is to 37.5 as 7 is to 15. The cross multiplication shown is 15 times 17.5 = 262.5 and 37.5 times 7 = 262.5.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 57.3863%;\"><\/td>\n<td style=\"width: 42.5%;\"><span id=\"eip-id1168468337952\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_022_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 57.3863%;\">To isolate \\(x\\), multiply both sides by the LCD, 63.<\/td>\n<td style=\"width: 42.5%;\"><span id=\"eip-id1168467155871\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_022_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 57.3863%;\">Simplify.<\/td>\n<td style=\"width: 42.5%;\"><span id=\"eip-id1168468412228\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_022_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 57.3863%;\">Divide the common factors.<\/td>\n<td style=\"width: 42.5%;\"><span id=\"eip-id1168467599001\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_022_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 57.3863%;\">Check: To check our answer, we substitute into the original proportion.<\/td>\n<td style=\"width: 42.5%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 57.3863%;\"><\/td>\n<td style=\"width: 42.5%;\"><span id=\"eip-id1168468458237\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_022_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 57.3863%;\" data-align=\"left\"><span id=\"eip-id1168468772331\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_023_img-09.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 42.5%;\"><span id=\"eip-id1168468781355\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_022_img-06.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 57.3863%;\">Show common factors.<\/td>\n<td style=\"width: 42.5%;\"><span id=\"eip-id1168468350523\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_022_img-07.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 57.3863%;\">Simplify.<\/td>\n<td style=\"width: 42.5%;\"><span id=\"eip-id1168468774250\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_022_img-08.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1468830\" data-type=\"problem\">\n<p id=\"fs-id1166495278671\">Solve the proportion: \\(\\frac{n}{84}=\\frac{11}{12}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166491297432\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1240488\">77<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166491401870\">When the variable is in a denominator, we\u2019ll use the fact that the <span class=\"no-emphasis\" data-type=\"term\">cross products<\/span> of a proportion are equal to solve the proportions.<\/p>\n<p id=\"eip-247\">We can find the cross products of the proportion and then set them equal. Then we solve the resulting equation using our familiar techniques.<\/p>\n\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-id1445776\" data-type=\"problem\">\n<p id=\"fs-id1251260\">Solve: \\(\\frac{144}{a}=\\frac{9}{4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1356436\" 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-id1166497245846\">Notice that the variable is in the denominator, so we will solve by finding the cross products and setting them equal.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\"><\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168469485492\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_02_024_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\">Find the cross products and set them equal.<\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168468280034\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_02_024_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\">Simplify.<\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168467308916\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_02_024_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\">Divide both sides by 9.<\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168468436933\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_02_024_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\">Simplify.<\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168468436950\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_02_024_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\">Check your answer:<\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168468436950\" data-type=\"media\" data-alt=\".\">\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\"><\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168468436950\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168468445856\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_025_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\">Substitute a = 64<\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168468436950\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168466275924\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_025_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\">Show common factors.<\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168468436950\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168469868535\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_025_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\">Simplify.<\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168468436950\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168469868535\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168467313516\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_025_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nAnother method to solve this would be to multiply both sides by the LCD, \\(4a\\). Try it and verify that you get the same solution.\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1236975\" data-type=\"problem\">\n<p id=\"fs-id1341194\">Solve the proportion: \\(\\frac{91}{b}=\\frac{7}{5}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id828983\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id994403\">65<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166492887513\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1096940\" data-type=\"exercise\">\n<div id=\"fs-id1684481\" data-type=\"solution\">\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-id1478962\" data-type=\"problem\">\n<p id=\"fs-id1217253\">Solve: \\(\\frac{52}{91}=\\frac{-4}{y}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1499285\" 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: 65.9086%;\" colspan=\"2\">Find the cross products and set them equal.<\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466200955\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_026_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 65.9086%;\" colspan=\"2\"><\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168469446628\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_026_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 65.9086%;\" colspan=\"2\">Simplify.<\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466590965\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_026_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 65.9086%;\" colspan=\"2\">Divide both sides by 52.<\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466126960\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_026_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466126977\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_026_img-06.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\"><strong>Check:<\/strong><\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466126977\" data-type=\"media\" data-alt=\".\">\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\"><\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466126977\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168465991847\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_027_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\"><span id=\"eip-id1168469440416\" data-type=\"media\" data-alt=\".\">Substitute y = \u22127\n<\/span><\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466126977\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168465991847\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168469631391\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_027_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\"><span id=\"eip-id1168469440416\" data-type=\"media\" data-alt=\".\">Show common factors.<\/span><\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466126977\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168465991847\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168469631391\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168469603779\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_027_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 65.9086%;\" colspan=\"2\"><span id=\"eip-id1168469440416\" data-type=\"media\" data-alt=\".\">Simplify.<\/span><\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466126977\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168465991847\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168469631391\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168469603779\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168466047201\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_027_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1154248\" data-type=\"problem\">\n<p id=\"fs-id2053972\">Solve the proportion: \\(\\frac{84}{98}=\\frac{-6}{x}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166497424916\" data-type=\"solution\"><details><summary>Show answer<\/summary>\u22127\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Solve Applications Using Proportions<\/h1>\nWhen we set up the <span class=\"no-emphasis\" data-type=\"term\">proportion<\/span>, we must make sure the units are correct\u2014the units in the numerators match and the units in the denominators match.\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-id1471445\" data-type=\"problem\">\n<p id=\"fs-id1166490858421\">When pediatricians prescribe acetaminophen to children, they prescribe \\(5\\) millilitres (ml) of acetaminophen for every \\(25\\) pounds of the child\u2019s weight. If Zoe weighs \\(80\\) pounds, how many millilitres of acetaminophen will her doctor prescribe?<\/p>\n\n<\/div>\n<div id=\"fs-id1486412\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468389749\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>How many ml of acetaminophen the doctor will prescribe<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let \\(a=\\) ml of acetaminophen.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>If 5 ml is prescribed for every 25 pounds, how much will be prescribed for 80 pounds?<\/td>\n<\/tr>\n<tr>\n<td>Translate into a proportion.<\/td>\n<td><span id=\"eip-id1168466156855\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_001_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute given values\u2014be careful of the units.<\/td>\n<td><span id=\"eip-id1168466091684\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_001_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by 80.<\/td>\n<td><span id=\"eip-id1168469591120\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_001_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply and show common factors.<\/td>\n<td><span id=\"eip-id1168469771390\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_001_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469832672\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_001_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check if the answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. Since 80 is about 3 times 25, the medicine should be about 3 times 5.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence.<\/td>\n<td>The pediatrician would prescribe 16 ml of acetaminophen to Zoe.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1407319\">You could also solve this proportion by setting the cross products equal.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166494585593\" data-type=\"problem\">\n<p id=\"fs-id1166497376317\">Pediatricians prescribe \\(5\\) millilitres (ml) of acetaminophen for every \\(25\\) pounds of a child\u2019s weight. How many millilitres of acetaminophen will the doctor prescribe for Emilia, who weighs \\(60\\) pounds?<\/p>\n\n<\/div>\n<div id=\"fs-id1693654\" data-type=\"solution\"><details><summary>Show answer<\/summary>12 ml\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-id1166495836173\" data-type=\"problem\">\n\nThe doctor prescribes for you to take 60 milligrams of the medication that is found in a liquid cough syrup.\u00a0 The label on the syrup reads 100 mg \/5 mL. How much cough syrup should you take?\n\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution\u00a0<\/strong><\/div>\n<table id=\"eip-id1168466068741\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>How much cough syrup you should take?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let \\(x=\\) amount of cough syrup.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>If there is 100 mg in 5 mL, then 60 mg is in what amount?<\/td>\n<\/tr>\n<tr>\n<td>Translate into a proportion.<\/td>\n<td>\\(\\frac{mg}{mL}=\\frac{mg}{mL}\\)<\/td>\n<\/tr>\n<tr>\n<td>Substitute given values.<\/td>\n<td>\\(\\frac{100}{5}=\\frac{60}{x}\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the cross product.<\/td>\n<td>\\(100 x = {5}\\cdot\\ {60}\\)<\/td>\n<\/tr>\n<tr>\n<td>Divide by 100.<\/td>\n<td><span id=\"eip-id1168467360492\" data-type=\"media\" data-alt=\".\">x = 3<\/span><\/td>\n<\/tr>\n<tr>\n<td>Check if the answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. Since 60 mg is less then 100 mg, than 3 mL is less that 5 mL.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence.<\/td>\n<td>You should take 3 mL of cough syrup.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nThe doctor prescribes 30 milligrams of the medication found in the liquid cough syrup to your daughter.\u00a0 The label on the syrup reads 100 mg \/5 mL. How much cough syrup you should give to your daughter?\n\nShow answer\n\n1.5 mL\n\n<\/div>\n<\/div>\n<div id=\"fs-id1166484085408\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1319706\" data-type=\"exercise\">\n<div id=\"fs-id1166478988848\" data-type=\"solution\">\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-id1166492709163\" data-type=\"problem\">\n<p id=\"fs-id1166490858582\">For adults over 18, the recommended daily allowance for protein is 0.8 grams per 1 kilogram of body weight. How many grams of protein is an adult allowed to consume per day if your weight is 68 kilograms?<\/p>\n\n<\/div>\n<div id=\"fs-id1166482704727\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168469868734\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>How many grams of protein is an adult allowed to consume per day?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let \\(p=\\) number of grams of protein.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>If 0.8 gr is allowed for 1 kg, then how many grams is allowed for 68 kg?<\/td>\n<\/tr>\n<tr>\n<td>Translate into a proportion.<\/td>\n<td><span id=\"eip-id1168468387263\" data-type=\"media\" data-alt=\".\">\\(\\frac{protein }{weight }=\\frac{protein }{weight }\\)<\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute given values.<\/td>\n<td><span id=\"eip-id1168467114088\" data-type=\"media\" data-alt=\".\">\\(\\frac{0.8}{1}=\\frac{p}{68}\\)<\/span><\/td>\n<\/tr>\n<tr>\n<td>The variable is in the denominator, so find the cross products and set them equal.<\/td>\n<td><span id=\"eip-id1168467352665\" data-type=\"media\" data-alt=\".\">\\(p\\cdot\\ {1}={0.8}\\cdot\\ {68}\\)\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>p = 54.4<\/td>\n<\/tr>\n<tr>\n<td>Check if the answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes, if the allowance\u00a0 would be 1 gram per 1 kilogram, it would be 68 grams a day.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence.<\/td>\n<td>An adult over 18 is allowed to consume 54.4 grams of protein.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1166492357407\">Base on example 8, how many grams of protein is Nicole allowed if her weight is 52 kilograms?<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1833449\">41.6 grams<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Write Percent Equations As Proportions<\/h1>\nThe proportion method for solving percent problems involves a percent proportion. A <strong data-effect=\"bold\">percent proportion<\/strong> is an equation where a percent is equal to an equivalent ratio.\n<p id=\"fs-id1166484174541\">For example, \\(\\text{60\\%}=\\frac{60}{100}\\) and we can simplify \\(\\frac{60}{100}=\\frac{3}{5}\\). Since the equation \\(\\frac{60}{100}=\\frac{3}{5}\\) shows a percent equal to an equivalent ratio, we call it a percent proportion. Using the vocabulary we used earlier:<\/p>\n\\(\\frac{\\text{amount}}{\\text{base}}=\\frac{\\text{percent}}{100}\\)\n<div id=\"fs-id1166484174543\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\phantom{\\rule{1.2em}{0ex}}\\frac{3}{5}=\\frac{60}{100}\\)<\/div>\n<div id=\"fs-id1166491221134\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Percent Proportion<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1166484058937\">The amount is to the base as the percent is to \\(100\\).<\/p>\n\\(\\frac{\\text{amount}}{\\text{base}}=\\frac{\\text{percent}}{100}\\)\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166490806604\">If we restate the problem in the words of a proportion, it may be easier to set up the proportion:<\/p>\n\\(\\mathit{\\text{The amount is to the base as the percent is to one hundred.}}\\)\n<p id=\"fs-id1512345\">We could also say:<\/p>\n\\(\\mathit{\\text{The amount out of the base is the same as the percent out of one hundred.}}\\)\n\nFirst we will practice translating into a percent proportion. Later, we\u2019ll solve the proportion.\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 data-type=\"problem\">\n<p id=\"fs-id1699747\">Translate to a proportion. What number is \\(\\text{75\\%}\\) of \\(90?\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1833179\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\nIf you look for the word \"of\", it may help you identify the base.\n<table id=\"eip-id1166828184051\" style=\"width: 100%;\" summary=\"The figure shows the parts of a percent proportion in the question 'What number is 75% of 90?' It shows 'what number' as the amount, 75% as the percent, and 90 as the base.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify the parts of the percent proportion.<\/td>\n<td><span id=\"eip-id1166821262634\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_013_img-01.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Restate as a proportion.<\/td>\n<td><span id=\"eip-id1166819463374\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_013_img-02.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Set up the proportion. Let \\(n=\\text{number}\\).<\/td>\n<td>\\(\\frac{n}{90}=\\frac{75}{100}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1506540\" data-type=\"problem\">\n\nTranslate to a proportion: What number is \\(\\text{60\\%}\\) of \\(105?\\)\n\n<\/div>\n<div id=\"fs-id1166491254241\" data-type=\"solution\"><details><summary>Show answer<\/summary>\\(\\frac{n}{105}=\\frac{60}{100}\\)\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1338834\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166497443440\" data-type=\"exercise\">\n<div id=\"fs-id1166484083290\" data-type=\"solution\">\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-id1395244\" data-type=\"problem\">\n<p id=\"fs-id1357256\">Translate to a proportion. \\(19\\) is \\(\\text{25\\%}\\) of what number?<\/p>\n\n<\/div>\n<div id=\"fs-id1482353\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id2096152\" style=\"width: 100%;\" summary=\"The figure shows the parts of a percent proportion in the question '19 is 25% of what number?' It shows 19 as the amount, 25% as the percent, and 'what number' as the base.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify the parts of the percent proportion.<\/td>\n<td><span id=\"eip-id2096344\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_014-01.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Restate as a proportion.<\/td>\n<td><span id=\"eip-id2096496\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_014-02.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Set up the proportion. Let \\(n=\\text{number}\\).<\/td>\n<td>\\(\\frac{19}{n}=\\frac{25}{100}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1956656\" data-type=\"problem\">\n<p id=\"fs-id1457910\">Translate to a proportion: \\(36\\) is \\(\\text{25\\%}\\) of what number?<\/p>\n\n<\/div>\n<div id=\"fs-id1948524\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1166491296749\">\\(\\frac{36}{n}=\\frac{25}{100}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1945455\" data-type=\"exercise\">\n<div id=\"fs-id1166493708780\" data-type=\"problem\">\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-id1456940\" data-type=\"problem\">\n<p id=\"fs-id1494096\">Translate to a proportion. What percent of \\(27\\) is \\(9?\\)<\/p>\n\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1166141441606\" style=\"width: 100%;\" summary=\"The figure shows the parts of a percent proportion in the question 'What percent of 27 is 9?' It shows 'what percent' as the percent, 27 as the base, and 9 as the amount.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify the parts of the percent proportion.<\/td>\n<td><span id=\"eip-id1166123041868\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_015_img-01.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Restate as a proportion.<\/td>\n<td><span id=\"eip-id1166129402544\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_015_img-02.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Set up the proportion. Let \\(p=\\text{percent}\\).<\/td>\n<td>\\(\\frac{9}{27}=\\frac{p}{100}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166492019228\" data-type=\"problem\">\n<p id=\"fs-id897900\">Translate to a proportion: What percent of \\(52\\) is \\(39?\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1480032\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1524754\">\\(\\frac{n}{100}=\\frac{39}{52}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Translate and Solve Percent Proportions<\/h1>\n<p id=\"fs-id1166484083924\">Now that we have written percent equations as proportions, we are ready to solve the equations.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1833323\" data-type=\"problem\">\n<p id=\"fs-id1166490855869\">A human body is made up of mostly water. As we age, total body water content also diminishes so that by the time we are in our eighties the percent of water in our bodies has decreased to around 45%. If your grandfather weights 80 kg, what number is the 45% of his weight?<\/p>\n\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id4251535\" style=\"width: 100%;\" summary=\"The figure shows the parts of a percent proportion in the question 'What number is 45% of 80?' It shows 'what number' as the amount, 45% as the percent, and 80 as the base.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify the parts of the percent proportion.<\/td>\n<td><span id=\"eip-id1167304133055\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_016_img-01.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Restate as a proportion.<\/td>\n<td><span id=\"eip-id3247756\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_016_img-02.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Set up the proportion. Let \\(n=\\) number.<\/td>\n<td><span id=\"eip-id1168469774887\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_004_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Find the cross products and set them equal.<\/td>\n<td><span id=\"eip-id1168467168393\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_004_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168464924388\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_004_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 100.<\/td>\n<td><span id=\"eip-id1168464924404\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_004_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168464917165\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_004_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check if the answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. 45 is a little less than half of 100 and 36 is a little less than half 80.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>36 kg is 45% of 80 kg.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1476032\" data-type=\"problem\">\n\nAdult male typically are composed of about 60% water. If a male weights 86 kg, what number is \\(\\text{60\\%}\\) of \\(86?\\)\n\n<\/div>\n<div id=\"fs-id1763000\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166492788865\">51.6 kg<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1465902\">In the next example, the percent is more than \\(100\\), which is more than one whole. So the unknown number will be more than the base.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166484085537\" data-type=\"problem\">\n<p id=\"fs-id1166483694550\">According to Wikipedia, the red blood cells of an average adult human male store collectively about 2.5 grams of iron. This represents 65% of the total iron contained in the body. Find the total amount of iron contained in the body. Round your answer to the nearest tenth.<\/p>\n\n<\/div>\n<div id=\"fs-id1166482688502\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution\u00a0<\/strong><\/div>\n<table id=\"eip-id1165358285731\" style=\"width: 100%;\" summary=\"The figure shows the parts of a percent proportion in the question '125% of 25 is what number?' It shows 125% as the percent, 25 as the base, and 'what number' as the amount.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify the parts of the percent proportion.<\/td>\n<td><span id=\"eip-id1165367323904\" data-type=\"media\" data-alt=\".\">65% = percent, 2.5 grams = amount,\u00a0 base = ?<\/span><\/td>\n<\/tr>\n<tr>\n<td>Restate as a proportion.<\/td>\n<td>65% of what number is 2.5<\/td>\n<\/tr>\n<tr>\n<td>Set up the proportion. Let \\(n=\\) number.<\/td>\n<td><span id=\"eip-id1168467114088\" data-type=\"media\" data-alt=\".\">\\(\\frac{65}{100}=\\frac{2.5}{n}\\)<\/span><\/td>\n<\/tr>\n<tr>\n<td>Find the cross products and set them equal.<\/td>\n<td><span id=\"eip-id1168468771212\" data-type=\"media\" data-alt=\".\">\\({65}{n}={100}\\cdot\\ {2.5}\\) \u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468464320\" data-type=\"media\" data-alt=\".\">65 n = 250<\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 65.<\/td>\n<td><span id=\"eip-id1168467114088\" data-type=\"media\" data-alt=\".\">\\(\\frac{65 n}{65}=\\frac{250}{65}\\)<\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>n = 3.8<\/td>\n<\/tr>\n<tr>\n<td>Check if the answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes.100% is more than 65% and 3.8 is more than 2.5.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The total amount of iron in the body of an average adult human male is 3.8 grams.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166490874428\" data-type=\"problem\">\n<p id=\"fs-id1249213\">Translate and solve using proportions: \\(\\text{70\\%}\\) of \\(64\\) is what number?<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166491296592\">44.8<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1297505\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1292318\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1241946\" data-type=\"problem\">\n<p id=\"fs-id1305046\">The daily recommended intake for potassium is 4700 grams. If a medium sized banana contains 425 grams of potassium, what percent of the daily recommended intake is that? Round to one decimal place.<\/p>\n\n<\/div>\n<div id=\"fs-id1445168\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1171789006462\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify the parts of the percent proportion.<\/td>\n<td>4700 = base, 425 = amount, percent = ?<span id=\"eip-id1171793496328\" data-type=\"media\" data-alt=\".\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Restate as a proportion.<\/td>\n<td>What percent of 4700 is 425?<\/td>\n<\/tr>\n<tr>\n<td>Set up the proportion. Let \\(n=\\) number.<\/td>\n<td><span id=\"eip-id1168467114088\" data-type=\"media\" data-alt=\".\">\\(\\frac{425}{4700}=\\frac{n}{100}\\)<\/span><\/td>\n<\/tr>\n<tr>\n<td>Find the cross products and set them equal.<\/td>\n<td><span id=\"eip-id1168468515434\" data-type=\"media\" data-alt=\".\">\\(4700 n = {425}\\cdot\\ {100}\\)<\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468515451\" data-type=\"media\" data-alt=\".\">4700 n = 42500<\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 4700.<\/td>\n<td><span id=\"eip-id1168467114088\" data-type=\"media\" data-alt=\".\">\\(\\frac{4700 n}{4700}=\\frac{42500}{4700}\\)<\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>n = 9<\/td>\n<\/tr>\n<tr>\n<td>Check if the answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. 9 is less than 10 and 425 is less than 470.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>425 is 9% of 4700.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1517371\" data-type=\"problem\">\n\nTranslate and solve using proportions: What percent of \\(72\\) is \\(27?\\)\n\n<\/div>\n<div id=\"fs-id1491140\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1438795\">37.5%<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1491140\" data-type=\"solution\">\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1166498049771\" data-bullet-style=\"bullet\">\n \t<li><strong>Proportion<\/strong>\n<ul id=\"eip-id4505152\">\n \t<li>A proportion is an equation of the form \\(\\frac{a}{b}=\\frac{c}{d}\\), where \\(b\\ne 0\\), \\(d\\ne 0\\).The proportion states two ratios or rates are equal. The proportion is read \u201c\\(a\\) is to \\(b\\), as \\(c\\) is to \\(d\\)\u201d.<\/li>\n<\/ul>\n<\/li>\n \t<li><strong>Cross Products of a Proportion<\/strong>\n<ul id=\"eip-id1166665440339\">\n \t<li>For any proportion of the form \\(\\frac{a}{b}=\\frac{c}{d}\\), where \\(b\\ne 0\\), its cross products are equal: \\(a\\cdot d=b\\cdot c\\).<\/li>\n<\/ul>\n<\/li>\n \t<li><strong>Percent Proportion<\/strong>\n<ul id=\"eip-id1166625630839\">\n \t<li>The amount is to the base as the percent is to 100. \\(\\frac{\\text{amount}}{\\text{base}}=\\frac{\\text{percent}}{100}\\)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1166490867506\">\n \t<dt>proportion<\/dt>\n \t<dd id=\"fs-id1166490867511\">A proportion is an equation of the form \\(\\frac{a}{b}=\\frac{c}{d}\\), where \\(b\\ne 0\\), \\(d\\ne 0\\).The proportion states two ratios or rates are equal. The proportion is read \u201c\\(a\\) is to \\(b\\), as \\(c\\) is to \\(d\\)\u201d.<\/dd>\n<\/dl>\n<\/div>\n<h1 data-type=\"title\">6.3 Exercise Set<\/h1>\n<p id=\"eip-388\">In the following exercises, write each sentence as a proportion.<\/p>\n\n<ol class=\"twocolumn\">\n \t<li>\\(4\\) is to \\(15\\) as \\(36\\) is to \\(135\\).<\/li>\n \t<li>\\(12\\) is to \\(5\\) as \\(96\\) is to \\(40\\).<\/li>\n<\/ol>\n<p id=\"fs-id1543474\">In the following exercises, determine whether each equation is a proportion.<\/p>\n\n<ol class=\"twocolumn\" start=\"3\">\n \t<li>\\(\\frac{7}{15}=\\frac{56}{120}\\)<\/li>\n \t<li>\\(\\frac{11}{6}=\\frac{21}{16}\\)<\/li>\n \t<li>\\(\\frac{12}{18}=\\frac{4.99}{7.56}\\)<\/li>\n \t<li>\\(\\frac{13.5}{8.5}=\\frac{31.05}{19.55}\\)<\/li>\n<\/ol>\n<p id=\"eip-940\">In the following exercises, solve each proportion.<\/p>\n\n<ol class=\"twocolumn\" start=\"7\">\n \t<li>\\(\\frac{x}{56}=\\frac{7}{8}\\)<\/li>\n \t<li>\\(\\frac{49}{63}=\\frac{z}{9}\\)<\/li>\n \t<li>\\(\\frac{5}{a}=\\frac{65}{117}\\)<\/li>\n \t<li>\\(\\frac{98}{154}=\\frac{-7}{p}\\)<\/li>\n \t<li>\\(\\frac{a}{-8}=\\frac{-42}{48}\\)<\/li>\n \t<li>\\(\\frac{2.6}{3.9}=\\frac{c}{3}\\)<\/li>\n \t<li>\\(\\frac{2.7}{j}=\\frac{0.9}{0.2}\\)<\/li>\n \t<li>\\(\\frac{\\frac{1}{2}}{1}=\\frac{m}{8}\\)<\/li>\n<\/ol>\n<p id=\"eip-371\">In the following exercises, solve the proportion problem.<\/p>\n\n<ol start=\"15\">\n \t<li>Pediatricians prescribe \\(5\\) millilitre s (ml) of acetaminophen for every \\(25\\) pounds of a child\u2019s weight. How many millilitres of acetaminophen will the doctor prescribe for Jocelyn, who weighs \\(45\\) pounds?<\/li>\n \t<li>At the gym, Carol takes her pulse for \\(10\\) sec and counts \\(19\\) beats. How many beats per minute is this? Has Carol met her target heart rate of \\(140\\) beats per minute?<\/li>\n \t<li>A new energy drink advertises \\(106\\) calories for \\(8\\) ounces. How many calories are in \\(12\\) ounces of the drink?<\/li>\n \t<li>Karen eats \\(\\frac{1}{2}\\) cup of oatmeal that counts for \\(2\\) points on her weight loss program. Her husband, Joe, can have \\(3\\) points of oatmeal for breakfast. How much oatmeal can he have?<\/li>\n \t<li>Brianna, who weighs \\(6\\) kg, just received her shots and needs a pain killer. The pain killer is prescribed for children at \\(15\\) milligrams (mg) for every \\(1\\) kilogram (kg) of the child\u2019s weight. How many milligrams will the doctor prescribe?<\/li>\n \t<li>Kevin wants to keep his heart rate at \\(160\\) beats per minute while training. During his workout he counts \\(27\\) beats in \\(10\\) seconds. How many beats per minute is this? Has Kevin met his target<\/li>\n \t<li>One brand of microwave popcorn has \\(120\\) calories per serving. A whole bag of this popcorn has \\(3.5\\) servings. How many calories are in a whole bag of this microwave popcorn?<\/li>\n \t<li>Marissa loves the Caramel Macchiato at the coffee shop. The \\(16\\) oz. medium size has \\(240\\) calories. How many calories will she get if she drinks the large \\(20\\) oz. size?<\/li>\n \t<li>For every \\(1\\) kilogram (kg) of a child\u2019s weight, pediatricians prescribe \\(15\\) milligrams (mg) of a fever reducer. If Isabella weighs \\(12\\) kg, how many milligrams of the fever reducer will the pediatrician prescribe?<\/li>\n<\/ol>\n<p id=\"eip-390\">In the following exercises, translate to a proportion.<\/p>\n\n<ol start=\"24\">\n \t<li>What number is \\(\\text{35\\%}\\) of \\(250?\\)<\/li>\n \t<li>\\(45\\) is \\(\\text{30\\%}\\) of what number?<\/li>\n \t<li>What percent of \\(85\\) is \\(17?\\)<\/li>\n<\/ol>\n<p id=\"eip-773\">In the following exercises, translate and solve using proportions.<\/p>\n\n<ol start=\"27\">\n \t<li>What number is \\(\\text{65\\%}\\) of \\(180?\\)<\/li>\n \t<li>\\(\\text{17\\%}\\) of what number is \\(\\text{\\7.65}?\\)<\/li>\n \t<li>What percent of \\(56\\) is \\(14?\\)<\/li>\n<\/ol>\n<h1>Answers<\/h1>\n<ol class=\"twocolumn\">\n \t<li>\\(\\frac{4}{15}=\\frac{36}{135}\\)<\/li>\n \t<li>\\(\\frac{12}{5}=\\frac{96}{40}\\)<\/li>\n \t<li>yes<\/li>\n \t<li>no<\/li>\n \t<li>no<\/li>\n \t<li>yes<\/li>\n \t<li>49<\/li>\n \t<li>47<\/li>\n \t<li>9<\/li>\n \t<li>-11<\/li>\n \t<li>7<\/li>\n \t<li>2<\/li>\n \t<li>0.6<\/li>\n \t<li>14.4<\/li>\n \t<li>9 ml<\/li>\n \t<li>114, no<\/li>\n \t<li>159 cal<\/li>\n \t<li>\\(\\frac{3}{4}\\phantom{\\rule{0.3em}{0ex}}\\text{cup}\\)<\/li>\n \t<li>90 mg<\/li>\n \t<li>162, no<\/li>\n \t<li>420 cal<\/li>\n \t<li>300 cal<\/li>\n \t<li>180 mg<\/li>\n \t<li>\\(\\frac{n}{250}=\\frac{35}{100}\\)<\/li>\n \t<li>\\(\\frac{45}{n}=\\frac{30}{100}\\)<\/li>\n \t<li>\\(\\frac{17}{85}=\\frac{p}{100}\\)<\/li>\n \t<li>117<\/li>\n \t<li>45<\/li>\n \t<li>25%<\/li>\n<\/ol>\n<h1>Attributions<\/h1>\n<ol>\n \t<li>This chapter has been adapted from \u201cSolve Proportions and their Applications\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, 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.<\/li>\n \t<li><a href=\"https:\/\/pressbooks.oer.hawaii.edu\/humannutrition2\/chapter\/2-the-cardiovascular-system\/\">OER.hawaii.edu<\/a><\/li>\n \t<li>Wikipedia<\/li>\n \t<li>\u00a0Government of Canada Statistics<\/li>\n<\/ol>","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 it is expected that you will be able to:<\/p>\n<ul>\n<li>Use the definition of proportion<\/li>\n<li>Solve proportions<\/li>\n<li>Solve applications using proportions<\/li>\n<li>Write percent equations as proportions<\/li>\n<li>Translate and solve percent proportions<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Use the Definition of Proportion<\/h1>\n<p id=\"fs-id1682902\">When two ratios or rates are equal, the equation relating them is called a proportion.<\/p>\n<div id=\"fs-id1878909\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Proportion<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1166492018126\">A proportion is an equation of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-956170b66c86da7bf9c392eca461afb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#99;&#125;&#123;&#100;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" style=\"vertical-align: -6px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9e513f13b9a8df15c1c7b7afc2702f88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#92;&#110;&#101;&#32;&#48;&#44;&#100;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p id=\"fs-id1166490779333\">The proportion states two ratios or rates are equal. The proportion is read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9bfc5302631e5bc4080144b52670d7a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#96;&#96;&#125;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\" \/> is to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>, as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> is to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b1da8e52635ff682ff7899609a599d74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#92;&#116;&#101;&#120;&#116;&#123;&#39;&#39;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166497354347\">The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-07b9374c4ae0e62e6b79f800bf9bb51e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"41\" style=\"vertical-align: -6px;\" \/> is a proportion because the two fractions are equal. The proportion <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-07b9374c4ae0e62e6b79f800bf9bb51e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"41\" style=\"vertical-align: -6px;\" \/> is read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7d4bca8f73ed942941573c4285ad8208_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#96;&#96;&#125;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"15\" style=\"vertical-align: -1px;\" \/> is to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> is to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-21af86a5d5b58a6afee9d41df737680e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#116;&#101;&#120;&#116;&#123;&#39;&#39;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/p>\n<p id=\"fs-id1166492788523\">If we compare quantities with units, we have to be sure we are comparing them in the right order.<\/p>\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-id1166494585692\" data-type=\"problem\">\n<p id=\"fs-id1287243\">Write the sentence as a proportion:<\/p>\n<p>72 heartbeats in 1 minute is the same as 216 heartbeats in 3 minutes.<\/p>\n<\/div>\n<div id=\"fs-id1166482132364\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468496922\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 39.2523%;\"><\/td>\n<td style=\"width: 60.7477%;\">72 is to 1 as 216 is to 3.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 39.2523%;\">Write as a proportion.<\/td>\n<td style=\"width: 60.7477%;\">\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3fc921c1a7631061914e3ee77f5b0b23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#55;&#50;&#32;&#104;&#101;&#97;&#114;&#116;&#98;&#101;&#97;&#116;&#115;&#125;&#125;&#32;&#32;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#32;&#109;&#105;&#110;&#117;&#116;&#101;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#49;&#54;&#32;&#104;&#101;&#97;&#114;&#116;&#98;&#101;&#97;&#116;&#115;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#32;&#109;&#105;&#110;&#117;&#116;&#101;&#115;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"198\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1166492788601\">Write the sentence as a proportion:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee6ea38acc4d74b3f255d3555f060df_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;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> is to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-930d01a5f622cee5952bab4752e56063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> is to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dce5a8d8a80b6aa9c2a9f6810851e582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<details>\n<summary>Show answer<\/summary>\n<div id=\"fs-id1956784\" data-type=\"solution\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f4972ebb1e7c12634159cf960f98236f_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;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#57;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#48;&#125;&#123;&#51;&#54;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"49\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/details>\n<\/div>\n<\/div>\n<p id=\"fs-id1097912\">Look at the proportions <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-07b9374c4ae0e62e6b79f800bf9bb51e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"41\" style=\"vertical-align: -6px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dcc16b5e3077160d0d012a7afd729fb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"41\" style=\"vertical-align: -6px;\" \/>. From our work with equivalent fractions we know these equations are true. But how do we know if an equation is a proportion with equivalent fractions if it contains fractions with larger numbers?<\/p>\n<p id=\"fs-id1166498443767\">To determine if a proportion is true, we find the <strong data-effect=\"bold\">cross products<\/strong> of each proportion. To find the cross products, we multiply each denominator with the opposite numerator (diagonally across the equal sign). The results are called a cross products because of the cross formed. The cross products of a proportion are equal.<\/p>\n<p><span id=\"fs-id1731746\" data-type=\"media\" data-alt=\"The figure shows cross multiplication of two proportions. There is the proportion 1 is to 2 as 4 is to 8. Arrows are shown diagonally across the equal sign to show cross products. The equations formed by cross multiplying are 8 \u00b7 1 = 8 and 2 \u00b7 4 = 8. There is the proportion 2 is to 3 as 6 is to 9. Arrows are shown diagonally across the equal sign to show cross products. The equations formed by cross multiplying are 9 \u00b7 2 = 18 and 3 \u00b7 6 = 18.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_028_img.jpg\" alt=\"The figure shows cross multiplication of two proportions. There is the proportion 1 is to 2 as 4 is to 8. Arrows are shown diagonally across the equal sign to show cross products. The equations formed by cross multiplying are 8 \u00b7 1 = 8 and 2 \u00b7 4 = 8. There is the proportion 2 is to 3 as 6 is to 9. Arrows are shown diagonally across the equal sign to show cross products. The equations formed by cross multiplying are 9 \u00b7 2 = 18 and 3 \u00b7 6 = 18.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<div id=\"fs-id1166489098476\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Cross Products of a Proportion<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1517408\">For any proportion of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-956170b66c86da7bf9c392eca461afb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#99;&#125;&#123;&#100;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" style=\"vertical-align: -6px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9e513f13b9a8df15c1c7b7afc2702f88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#92;&#110;&#101;&#32;&#48;&#44;&#100;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -4px;\" \/>, its cross products are equal.<\/p>\n<p><span id=\"fs-id1166494770801\" data-type=\"media\" data-alt=\"No Alt Text\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_003_img.jpg\" alt=\"No Alt Text\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1501697\">Cross products can be used to test whether a proportion is true. To test whether an equation makes a proportion, we find the cross products. If they are the equal, we have a proportion.<\/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-id1476424\" data-type=\"problem\">\n<p id=\"fs-id1166497362535\">Determine whether each equation is a proportion:<\/p>\n<ol id=\"eip-id1168466230295\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4065bd6016c1add85cf44793d52691a3_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;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#57;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#125;&#123;&#50;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"49\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6e4f2cbe512bf499d974aa6b5fd87f93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#55;&#46;&#53;&#125;&#123;&#51;&#55;&#46;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"66\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1946221\" data-type=\"solution\">\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1491625\">To determine if the equation is a proportion, we find the cross products. If they are equal, the equation is a proportion.<\/p>\n<table id=\"eip-id1168468703669\" style=\"width: 100%;\" summary=\"The figure shows the steps to finding the cross products of the proportion 4 is to 9 as 12 is to 28. The cross multiplication shown is 28 times 4 = 112 and 9 times 12 = 28.\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467196647\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_020_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Find the cross products.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6715eac2d8a7bad9c59576b16c700bf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#61;&#49;&#49;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#57;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#50;&#61;&#49;&#48;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"215\" style=\"vertical-align: -1px;\" \/><\/p>\n<p><span data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_020_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166481190972\">Since the cross products are not equal, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cd8dd34f7000bcc94c95527b7a589634_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#56;&#92;&#99;&#100;&#111;&#116;&#52;&#92;&#110;&#101;&#32;&#57;&#92;&#99;&#100;&#111;&#116;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"102\" style=\"vertical-align: -4px;\" \/>, the equation is not a proportion.<\/p>\n<table id=\"eip-id1168469699712\" style=\"width: 100%;\" summary=\"The figure shows the steps to finding the cross products of the proportion 17.5 is to 37.5 as 7 is to 15. The cross multiplication shown is 15 times 17.5 = 262.5 and 37.5 times 7 = 262.5.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 28.6363%;\">b)<\/td>\n<td style=\"width: 71.25%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 28.6363%;\"><\/td>\n<td style=\"width: 71.25%;\"><span id=\"eip-id1168469613430\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_021_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 28.6363%;\">Find the cross products.<\/td>\n<td style=\"width: 71.25%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7694024e52efeb9094449135fbc266a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#55;&#46;&#53;&#61;&#50;&#54;&#50;&#46;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#55;&#46;&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#61;&#50;&#54;&#50;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"277\" style=\"vertical-align: -1px;\" \/><\/p>\n<p><span id=\"eip-id1168466166406\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_021_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1956342\">Since the cross products are equal, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b8d7adedae060844a7a61374459d29a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#92;&#99;&#100;&#111;&#116;&#49;&#55;&#46;&#53;&#61;&#51;&#55;&#46;&#53;&#92;&#99;&#100;&#111;&#116;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"138\" style=\"vertical-align: 0px;\" \/>, the equation is a proportion.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1431411\" data-type=\"problem\">\n<p id=\"fs-id1359170\">Determine whether each equation is a proportion:<\/p>\n<ol id=\"eip-id1168468436941\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-467e953b59bb6ad1e69544a300b6cd03_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;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#57;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#52;&#125;&#123;&#55;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"49\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4fd9aa829a401c6ff0eeffde10c7de54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#52;&#46;&#53;&#125;&#123;&#52;&#53;&#46;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"66\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ol>\n<\/div>\n<details>\n<summary>Show answer<\/summary>\n<div id=\"fs-id1166482688691\" data-type=\"solution\">\n<ol id=\"eip-id1168468413917\" class=\"circled\" type=\"a\">\n<li>no<\/li>\n<li>yes<\/li>\n<\/ol>\n<\/div>\n<\/details>\n<\/div>\n<\/div>\n<h1>Solve Proportions<\/h1>\n<p id=\"fs-id1166491085133\">To solve a proportion containing a variable, we remember that the proportion is an equation. All of the techniques we have used so far to solve equations still apply. In the next example, we will solve a proportion by multiplying by the <span class=\"no-emphasis\" data-type=\"term\">Least Common Denominator<\/span> (LCD) using the <span class=\"no-emphasis\" data-type=\"term\">Multiplication Property of Equality<\/span>.<\/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-id1944367\" data-type=\"problem\">\n<p id=\"fs-id1166494756631\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-68a31396e17c7df28397bd25201ca0ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#54;&#51;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1626522\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468652606\" style=\"width: 100%;\" summary=\"The figure shows the steps to finding the cross products of the proportion 17.5 is to 37.5 as 7 is to 15. The cross multiplication shown is 15 times 17.5 = 262.5 and 37.5 times 7 = 262.5.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 57.3863%;\"><\/td>\n<td style=\"width: 42.5%;\"><span id=\"eip-id1168468337952\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_022_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 57.3863%;\">To isolate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>, multiply both sides by the LCD, 63.<\/td>\n<td style=\"width: 42.5%;\"><span id=\"eip-id1168467155871\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_022_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 57.3863%;\">Simplify.<\/td>\n<td style=\"width: 42.5%;\"><span id=\"eip-id1168468412228\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_022_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 57.3863%;\">Divide the common factors.<\/td>\n<td style=\"width: 42.5%;\"><span id=\"eip-id1168467599001\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_022_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 57.3863%;\">Check: To check our answer, we substitute into the original proportion.<\/td>\n<td style=\"width: 42.5%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 57.3863%;\"><\/td>\n<td style=\"width: 42.5%;\"><span id=\"eip-id1168468458237\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_022_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 57.3863%;\" data-align=\"left\"><span id=\"eip-id1168468772331\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_023_img-09.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 42.5%;\"><span id=\"eip-id1168468781355\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_022_img-06.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 57.3863%;\">Show common factors.<\/td>\n<td style=\"width: 42.5%;\"><span id=\"eip-id1168468350523\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_022_img-07.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 57.3863%;\">Simplify.<\/td>\n<td style=\"width: 42.5%;\"><span id=\"eip-id1168468774250\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_022_img-08.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1468830\" data-type=\"problem\">\n<p id=\"fs-id1166495278671\">Solve the proportion: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-50bfe0ff9ceaf35c2cab953788fed014_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#110;&#125;&#123;&#56;&#52;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"55\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166491297432\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1240488\">77<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166491401870\">When the variable is in a denominator, we\u2019ll use the fact that the <span class=\"no-emphasis\" data-type=\"term\">cross products<\/span> of a proportion are equal to solve the proportions.<\/p>\n<p id=\"eip-247\">We can find the cross products of the proportion and then set them equal. Then we solve the resulting equation using our familiar techniques.<\/p>\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-id1445776\" data-type=\"problem\">\n<p id=\"fs-id1251260\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-010a33bcbc8dd5db93a14572df441a85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#52;&#52;&#125;&#123;&#97;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"55\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1356436\" 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-id1166497245846\">Notice that the variable is in the denominator, so we will solve by finding the cross products and setting them equal.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\"><\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168469485492\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_02_024_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\">Find the cross products and set them equal.<\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168468280034\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_02_024_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\">Simplify.<\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168467308916\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_02_024_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\">Divide both sides by 9.<\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168468436933\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_02_024_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\">Simplify.<\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168468436950\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_02_024_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\">Check your answer:<\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168468436950\" data-type=\"media\" data-alt=\".\">\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\"><\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168468436950\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168468445856\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_025_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\">Substitute a = 64<\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168468436950\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168466275924\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_025_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\">Show common factors.<\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168468436950\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168469868535\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_025_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.3114%;\" colspan=\"2\">Simplify.<\/td>\n<td style=\"width: 46.5921%;\"><span id=\"eip-id1168468436950\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168469868535\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168467313516\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_025_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Another method to solve this would be to multiply both sides by the LCD, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a73d28934f7d95ef97a09ad34d18e93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/>. Try it and verify that you get the same solution.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1236975\" data-type=\"problem\">\n<p id=\"fs-id1341194\">Solve the proportion: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-905ace97f27332ee102c14e59cb6b579_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#49;&#125;&#123;&#98;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id828983\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id994403\">65<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166492887513\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1096940\" data-type=\"exercise\">\n<div id=\"fs-id1684481\" data-type=\"solution\">\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-id1478962\" data-type=\"problem\">\n<p id=\"fs-id1217253\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c5ccbc44305df72c0e6bcbe89de8a802_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#50;&#125;&#123;&#57;&#49;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#52;&#125;&#123;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"59\" style=\"vertical-align: -9px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1499285\" 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: 65.9086%;\" colspan=\"2\">Find the cross products and set them equal.<\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466200955\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_026_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 65.9086%;\" colspan=\"2\"><\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168469446628\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_026_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 65.9086%;\" colspan=\"2\">Simplify.<\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466590965\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_026_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 65.9086%;\" colspan=\"2\">Divide both sides by 52.<\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466126960\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_026_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466126977\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_026_img-06.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\"><strong>Check:<\/strong><\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466126977\" data-type=\"media\" data-alt=\".\">\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\"><\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466126977\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168465991847\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_027_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\"><span id=\"eip-id1168469440416\" data-type=\"media\" data-alt=\".\">Substitute y = \u22127<br \/>\n<\/span><\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466126977\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168465991847\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168469631391\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_027_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\"><span id=\"eip-id1168469440416\" data-type=\"media\" data-alt=\".\">Show common factors.<\/span><\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466126977\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168465991847\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168469631391\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168469603779\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_027_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 65.9086%;\" colspan=\"2\"><span id=\"eip-id1168469440416\" data-type=\"media\" data-alt=\".\">Simplify.<\/span><\/td>\n<td style=\"width: 34.1122%;\"><span id=\"eip-id1168466126977\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168465991847\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168469631391\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168469603779\" data-type=\"media\" data-alt=\".\"><span id=\"eip-id1168466047201\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_027_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1154248\" data-type=\"problem\">\n<p id=\"fs-id2053972\">Solve the proportion: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-654fd64a0896251b774d84ef80449165_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#52;&#125;&#123;&#57;&#56;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#54;&#125;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"59\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166497424916\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p>\u22127<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Solve Applications Using Proportions<\/h1>\n<p>When we set up the <span class=\"no-emphasis\" data-type=\"term\">proportion<\/span>, we must make sure the units are correct\u2014the units in the numerators match and the units in the denominators match.<\/p>\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-id1471445\" data-type=\"problem\">\n<p id=\"fs-id1166490858421\">When pediatricians prescribe acetaminophen to children, they prescribe <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> millilitres (ml) of acetaminophen for every <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dd40a7f142c1fc4152e724db5432f76b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> pounds of the child\u2019s weight. If Zoe weighs <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-85d2fe3dc632ffa22ca593406cbf160d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> pounds, how many millilitres of acetaminophen will her doctor prescribe?<\/p>\n<\/div>\n<div id=\"fs-id1486412\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468389749\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>How many ml of acetaminophen the doctor will prescribe<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6fdf9894e43ac86e8b63ba96c72e7181_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"27\" style=\"vertical-align: 0px;\" \/> ml of acetaminophen.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>If 5 ml is prescribed for every 25 pounds, how much will be prescribed for 80 pounds?<\/td>\n<\/tr>\n<tr>\n<td>Translate into a proportion.<\/td>\n<td><span id=\"eip-id1168466156855\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_001_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute given values\u2014be careful of the units.<\/td>\n<td><span id=\"eip-id1168466091684\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_001_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by 80.<\/td>\n<td><span id=\"eip-id1168469591120\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_001_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply and show common factors.<\/td>\n<td><span id=\"eip-id1168469771390\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_001_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469832672\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_001_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check if the answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. Since 80 is about 3 times 25, the medicine should be about 3 times 5.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence.<\/td>\n<td>The pediatrician would prescribe 16 ml of acetaminophen to Zoe.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1407319\">You could also solve this proportion by setting the cross products equal.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166494585593\" data-type=\"problem\">\n<p id=\"fs-id1166497376317\">Pediatricians prescribe <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> millilitres (ml) of acetaminophen for every <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dd40a7f142c1fc4152e724db5432f76b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> pounds of a child\u2019s weight. How many millilitres of acetaminophen will the doctor prescribe for Emilia, who weighs <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7029ea134aa43ac5ffd9f780e196307d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> pounds?<\/p>\n<\/div>\n<div id=\"fs-id1693654\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p>12 ml<\/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-id1166495836173\" data-type=\"problem\">\n<p>The doctor prescribes for you to take 60 milligrams of the medication that is found in a liquid cough syrup.\u00a0 The label on the syrup reads 100 mg \/5 mL. How much cough syrup should you take?<\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution\u00a0<\/strong><\/div>\n<table id=\"eip-id1168466068741\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>How much cough syrup you should take?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e7bbcde7229c9d7d6f7f2b6793961e97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"28\" style=\"vertical-align: 0px;\" \/> amount of cough syrup.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>If there is 100 mg in 5 mL, then 60 mg is in what amount?<\/td>\n<\/tr>\n<tr>\n<td>Translate into a proportion.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aa52220fd575ce536ce52cd57539ae21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#109;&#103;&#125;&#123;&#109;&#76;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#109;&#103;&#125;&#123;&#109;&#76;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"71\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Substitute given values.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c7bc11cf012bf6b9caa7946f6a7709a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#48;&#125;&#123;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#48;&#125;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the cross product.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-14bd8a23349a9f14200d8e69dd75b161_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#48;&#32;&#120;&#32;&#61;&#32;&#123;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#32;&#123;&#54;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"105\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide by 100.<\/td>\n<td><span id=\"eip-id1168467360492\" data-type=\"media\" data-alt=\".\">x = 3<\/span><\/td>\n<\/tr>\n<tr>\n<td>Check if the answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. Since 60 mg is less then 100 mg, than 3 mL is less that 5 mL.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence.<\/td>\n<td>You should take 3 mL of cough syrup.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>The doctor prescribes 30 milligrams of the medication found in the liquid cough syrup to your daughter.\u00a0 The label on the syrup reads 100 mg \/5 mL. How much cough syrup you should give to your daughter?<\/p>\n<p>Show answer<\/p>\n<p>1.5 mL<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1166484085408\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1319706\" data-type=\"exercise\">\n<div id=\"fs-id1166478988848\" data-type=\"solution\">\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-id1166492709163\" data-type=\"problem\">\n<p id=\"fs-id1166490858582\">For adults over 18, the recommended daily allowance for protein is 0.8 grams per 1 kilogram of body weight. How many grams of protein is an adult allowed to consume per day if your weight is 68 kilograms?<\/p>\n<\/div>\n<div id=\"fs-id1166482704727\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168469868734\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>How many grams of protein is an adult allowed to consume per day?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> number of grams of protein.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>If 0.8 gr is allowed for 1 kg, then how many grams is allowed for 68 kg?<\/td>\n<\/tr>\n<tr>\n<td>Translate into a proportion.<\/td>\n<td><span id=\"eip-id1168468387263\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-acbef8823ab67871ee36dc2fdf39d9e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#112;&#114;&#111;&#116;&#101;&#105;&#110;&#32;&#125;&#123;&#119;&#101;&#105;&#103;&#104;&#116;&#32;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#112;&#114;&#111;&#116;&#101;&#105;&#110;&#32;&#125;&#123;&#119;&#101;&#105;&#103;&#104;&#116;&#32;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"118\" style=\"vertical-align: -9px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute given values.<\/td>\n<td><span id=\"eip-id1168467114088\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-50fe83b36764d04552603dec5678c7cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#46;&#56;&#125;&#123;&#49;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#112;&#125;&#123;&#54;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"59\" style=\"vertical-align: -6px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>The variable is in the denominator, so find the cross products and set them equal.<\/td>\n<td><span id=\"eip-id1168467352665\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-56dc04e9c03bd472e1faa200b658d159_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#92;&#99;&#100;&#111;&#116;&#92;&#32;&#123;&#49;&#125;&#61;&#123;&#48;&#46;&#56;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#32;&#123;&#54;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"120\" style=\"vertical-align: -4px;\" \/>\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>p = 54.4<\/td>\n<\/tr>\n<tr>\n<td>Check if the answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes, if the allowance\u00a0 would be 1 gram per 1 kilogram, it would be 68 grams a day.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence.<\/td>\n<td>An adult over 18 is allowed to consume 54.4 grams of protein.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1166492357407\">Base on example 8, how many grams of protein is Nicole allowed if her weight is 52 kilograms?<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1833449\">41.6 grams<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Write Percent Equations As Proportions<\/h1>\n<p>The proportion method for solving percent problems involves a percent proportion. A <strong data-effect=\"bold\">percent proportion<\/strong> is an equation where a percent is equal to an equivalent ratio.<\/p>\n<p id=\"fs-id1166484174541\">For example, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5836684d7aa98bab4e067b86034aabfc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#92;&#37;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#48;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"79\" style=\"vertical-align: -6px;\" \/> and we can simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-035f016e728c32d095aa3668cf4fec29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#48;&#125;&#123;&#49;&#48;&#48;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"55\" style=\"vertical-align: -7px;\" \/>. Since the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-035f016e728c32d095aa3668cf4fec29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#48;&#125;&#123;&#49;&#48;&#48;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"55\" style=\"vertical-align: -7px;\" \/> shows a percent equal to an equivalent ratio, we call it a percent proportion. Using the vocabulary we used earlier:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a2203f3a3e3ac4f1de287dbadb9cfb37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#109;&#111;&#117;&#110;&#116;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#97;&#115;&#101;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#101;&#114;&#99;&#101;&#110;&#116;&#125;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"118\" style=\"vertical-align: -7px;\" \/><\/p>\n<div id=\"fs-id1166484174543\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1b44eefdf2167d8271eb692e5a6e6219_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;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#48;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"56\" style=\"vertical-align: -7px;\" \/><\/div>\n<div id=\"fs-id1166491221134\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Percent Proportion<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1166484058937\">The amount is to the base as the percent is to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2c4b0a8a79b7bd0e6e72a5fca0be9982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a2203f3a3e3ac4f1de287dbadb9cfb37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#109;&#111;&#117;&#110;&#116;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#97;&#115;&#101;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#101;&#114;&#99;&#101;&#110;&#116;&#125;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"118\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166490806604\">If we restate the problem in the words of a proportion, it may be easier to set up the proportion:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b97c15e3919d6be3079335246f97d5a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#105;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#32;&#97;&#109;&#111;&#117;&#110;&#116;&#32;&#105;&#115;&#32;&#116;&#111;&#32;&#116;&#104;&#101;&#32;&#98;&#97;&#115;&#101;&#32;&#97;&#115;&#32;&#116;&#104;&#101;&#32;&#112;&#101;&#114;&#99;&#101;&#110;&#116;&#32;&#105;&#115;&#32;&#116;&#111;&#32;&#111;&#110;&#101;&#32;&#104;&#117;&#110;&#100;&#114;&#101;&#100;&#46;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"466\" style=\"vertical-align: -3px;\" \/><\/p>\n<p id=\"fs-id1512345\">We could also say:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7a9d8eabca0384d3b7b581a9d013f8be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#105;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#32;&#97;&#109;&#111;&#117;&#110;&#116;&#32;&#111;&#117;&#116;&#32;&#111;&#102;&#32;&#116;&#104;&#101;&#32;&#98;&#97;&#115;&#101;&#32;&#105;&#115;&#32;&#116;&#104;&#101;&#32;&#115;&#97;&#109;&#101;&#32;&#97;&#115;&#32;&#116;&#104;&#101;&#32;&#112;&#101;&#114;&#99;&#101;&#110;&#116;&#32;&#111;&#117;&#116;&#32;&#111;&#102;&#32;&#111;&#110;&#101;&#32;&#104;&#117;&#110;&#100;&#114;&#101;&#100;&#46;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"583\" style=\"vertical-align: -3px;\" \/><\/p>\n<p>First we will practice translating into a percent proportion. Later, we\u2019ll solve the proportion.<\/p>\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 data-type=\"problem\">\n<p id=\"fs-id1699747\">Translate to a proportion. What number is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-78ab94a84251f659e623130f06660e8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#55;&#53;&#92;&#37;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"32\" style=\"vertical-align: -1px;\" \/> of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9409fb3097bbb0ca966818de15b8faf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#48;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1833179\" 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>If you look for the word &#8220;of&#8221;, it may help you identify the base.<\/p>\n<table id=\"eip-id1166828184051\" style=\"width: 100%;\" summary=\"The figure shows the parts of a percent proportion in the question 'What number is 75% of 90?' It shows 'what number' as the amount, 75% as the percent, and 90 as the base.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify the parts of the percent proportion.<\/td>\n<td><span id=\"eip-id1166821262634\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_013_img-01.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Restate as a proportion.<\/td>\n<td><span id=\"eip-id1166819463374\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_013_img-02.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Set up the proportion. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aa2d70b2f7cf81922b9544762b74c24c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#117;&#109;&#98;&#101;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"93\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4d41d453898f291d33c5b309b001e0c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#110;&#125;&#123;&#57;&#48;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#53;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"62\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1506540\" data-type=\"problem\">\n<p>Translate to a proportion: What number is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f01c40b1c9b8da1b69b24764898576e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#92;&#37;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"32\" style=\"vertical-align: -1px;\" \/> of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-eea5bfc0220fde5e3866d3ac6972e932_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#53;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"34\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1166491254241\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-272c20db48c51442dfa6434d8f66b07a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#110;&#125;&#123;&#49;&#48;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#48;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"69\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1338834\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166497443440\" data-type=\"exercise\">\n<div id=\"fs-id1166484083290\" data-type=\"solution\">\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-id1395244\" data-type=\"problem\">\n<p id=\"fs-id1357256\">Translate to a proportion. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-23ae1c0b89342725f5c66b11294f8bcc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-999170fba948bd6fdce99990751ba6b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#53;&#92;&#37;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"32\" style=\"vertical-align: -1px;\" \/> of what number?<\/p>\n<\/div>\n<div id=\"fs-id1482353\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id2096152\" style=\"width: 100%;\" summary=\"The figure shows the parts of a percent proportion in the question '19 is 25% of what number?' It shows 19 as the amount, 25% as the percent, and 'what number' as the base.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify the parts of the percent proportion.<\/td>\n<td><span id=\"eip-id2096344\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_014-01.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Restate as a proportion.<\/td>\n<td><span id=\"eip-id2096496\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_014-02.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Set up the proportion. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aa2d70b2f7cf81922b9544762b74c24c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#117;&#109;&#98;&#101;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"93\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b51bad0543aa1db668d4c6468ed5dd87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#57;&#125;&#123;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"62\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1956656\" data-type=\"problem\">\n<p id=\"fs-id1457910\">Translate to a proportion: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dce5a8d8a80b6aa9c2a9f6810851e582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-999170fba948bd6fdce99990751ba6b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#53;&#92;&#37;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"32\" style=\"vertical-align: -1px;\" \/> of what number?<\/p>\n<\/div>\n<div id=\"fs-id1948524\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166491296749\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d7e1995c9622e370e35aed647762650f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#54;&#125;&#123;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"62\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1945455\" data-type=\"exercise\">\n<div id=\"fs-id1166493708780\" data-type=\"problem\">\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-id1456940\" data-type=\"problem\">\n<p id=\"fs-id1494096\">Translate to a proportion. What percent of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a7b50e6fd02515483149eb902ea18dfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5b9ab147a10432cef90cf0b375b9d6e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1166141441606\" style=\"width: 100%;\" summary=\"The figure shows the parts of a percent proportion in the question 'What percent of 27 is 9?' It shows 'what percent' as the percent, 27 as the base, and 9 as the amount.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify the parts of the percent proportion.<\/td>\n<td><span id=\"eip-id1166123041868\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_015_img-01.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Restate as a proportion.<\/td>\n<td><span id=\"eip-id1166129402544\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_015_img-02.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Set up the proportion. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e34bbf82bfc3b4d8b8c5c4bc3f3acc25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#101;&#114;&#99;&#101;&#110;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"90\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5523044684c5bae782b1a823d80d35a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#50;&#55;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#112;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"62\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166492019228\" data-type=\"problem\">\n<p id=\"fs-id897900\">Translate to a proportion: What percent of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-30352d66e4a511eedaaaf1c7497a30c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d123e402b95e01100ede4a195046cc6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#57;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1480032\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1524754\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3e486ea03b0878c696cd93fd13263522_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#110;&#125;&#123;&#49;&#48;&#48;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#57;&#125;&#123;&#53;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"62\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Translate and Solve Percent Proportions<\/h1>\n<p id=\"fs-id1166484083924\">Now that we have written percent equations as proportions, we are ready to solve the equations.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1833323\" data-type=\"problem\">\n<p id=\"fs-id1166490855869\">A human body is made up of mostly water. As we age, total body water content also diminishes so that by the time we are in our eighties the percent of water in our bodies has decreased to around 45%. If your grandfather weights 80 kg, what number is the 45% of his weight?<\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id4251535\" style=\"width: 100%;\" summary=\"The figure shows the parts of a percent proportion in the question 'What number is 45% of 80?' It shows 'what number' as the amount, 45% as the percent, and 80 as the base.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify the parts of the percent proportion.<\/td>\n<td><span id=\"eip-id1167304133055\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_016_img-01.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Restate as a proportion.<\/td>\n<td><span id=\"eip-id3247756\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_016_img-02.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Set up the proportion. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> number.<\/td>\n<td><span id=\"eip-id1168469774887\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_004_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Find the cross products and set them equal.<\/td>\n<td><span id=\"eip-id1168467168393\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_004_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168464924388\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_004_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 100.<\/td>\n<td><span id=\"eip-id1168464924404\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_004_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168464917165\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/06\/CNX_BMath_Figure_06_05_004_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check if the answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. 45 is a little less than half of 100 and 36 is a little less than half 80.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>36 kg is 45% of 80 kg.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1476032\" data-type=\"problem\">\n<p>Adult male typically are composed of about 60% water. If a male weights 86 kg, what number is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f01c40b1c9b8da1b69b24764898576e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#92;&#37;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"32\" style=\"vertical-align: -1px;\" \/> of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f8d759edc998e5ad8afd165db060ced2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#54;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1763000\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166492788865\">51.6 kg<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1465902\">In the next example, the percent is more than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2c4b0a8a79b7bd0e6e72a5fca0be9982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/>, which is more than one whole. So the unknown number will be more than the base.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166484085537\" data-type=\"problem\">\n<p id=\"fs-id1166483694550\">According to Wikipedia, the red blood cells of an average adult human male store collectively about 2.5 grams of iron. This represents 65% of the total iron contained in the body. Find the total amount of iron contained in the body. Round your answer to the nearest tenth.<\/p>\n<\/div>\n<div id=\"fs-id1166482688502\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution\u00a0<\/strong><\/div>\n<table id=\"eip-id1165358285731\" style=\"width: 100%;\" summary=\"The figure shows the parts of a percent proportion in the question '125% of 25 is what number?' It shows 125% as the percent, 25 as the base, and 'what number' as the amount.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify the parts of the percent proportion.<\/td>\n<td><span id=\"eip-id1165367323904\" data-type=\"media\" data-alt=\".\">65% = percent, 2.5 grams = amount,\u00a0 base = ?<\/span><\/td>\n<\/tr>\n<tr>\n<td>Restate as a proportion.<\/td>\n<td>65% of what number is 2.5<\/td>\n<\/tr>\n<tr>\n<td>Set up the proportion. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> number.<\/td>\n<td><span id=\"eip-id1168467114088\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bed315797bea33d457ad20d6ae30b440_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#53;&#125;&#123;&#49;&#48;&#48;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#46;&#53;&#125;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Find the cross products and set them equal.<\/td>\n<td><span id=\"eip-id1168468771212\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-72530fd6853acae2ce50c80cdc787009_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#54;&#53;&#125;&#123;&#110;&#125;&#61;&#123;&#49;&#48;&#48;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#32;&#123;&#50;&#46;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"119\" style=\"vertical-align: 0px;\" \/> \u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468464320\" data-type=\"media\" data-alt=\".\">65 n = 250<\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 65.<\/td>\n<td><span id=\"eip-id1168467114088\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-93c0d6942c9e6e7543936f72da25d1fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#53;&#32;&#110;&#125;&#123;&#54;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#48;&#125;&#123;&#54;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>n = 3.8<\/td>\n<\/tr>\n<tr>\n<td>Check if the answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes.100% is more than 65% and 3.8 is more than 2.5.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The total amount of iron in the body of an average adult human male is 3.8 grams.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166490874428\" data-type=\"problem\">\n<p id=\"fs-id1249213\">Translate and solve using proportions: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2c13c6986b7d5d5bdb31a962da1d84bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#55;&#48;&#92;&#37;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"32\" style=\"vertical-align: -1px;\" \/> of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-de25eb06760758d2c59eb63fca270413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> is what number?<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166491296592\">44.8<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1297505\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1292318\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1241946\" data-type=\"problem\">\n<p id=\"fs-id1305046\">The daily recommended intake for potassium is 4700 grams. If a medium sized banana contains 425 grams of potassium, what percent of the daily recommended intake is that? Round to one decimal place.<\/p>\n<\/div>\n<div id=\"fs-id1445168\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1171789006462\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>Identify the parts of the percent proportion.<\/td>\n<td>4700 = base, 425 = amount, percent = ?<span id=\"eip-id1171793496328\" data-type=\"media\" data-alt=\".\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Restate as a proportion.<\/td>\n<td>What percent of 4700 is 425?<\/td>\n<\/tr>\n<tr>\n<td>Set up the proportion. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> number.<\/td>\n<td><span id=\"eip-id1168467114088\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-51b6bbe0a8fffa0dc4d14bcf0d370f74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#50;&#53;&#125;&#123;&#52;&#55;&#48;&#48;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#110;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"76\" style=\"vertical-align: -6px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Find the cross products and set them equal.<\/td>\n<td><span id=\"eip-id1168468515434\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9fe140fb548e14f732dbd3b3497b54fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#55;&#48;&#48;&#32;&#110;&#32;&#61;&#32;&#123;&#52;&#50;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#32;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"142\" style=\"vertical-align: 0px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468515451\" data-type=\"media\" data-alt=\".\">4700 n = 42500<\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 4700.<\/td>\n<td><span id=\"eip-id1168467114088\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c2efed785a4be02ef0e30360979032e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#55;&#48;&#48;&#32;&#110;&#125;&#123;&#52;&#55;&#48;&#48;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#50;&#53;&#48;&#48;&#125;&#123;&#52;&#55;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"98\" style=\"vertical-align: -6px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>n = 9<\/td>\n<\/tr>\n<tr>\n<td>Check if the answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. 9 is less than 10 and 425 is less than 470.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>425 is 9% of 4700.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1517371\" data-type=\"problem\">\n<p>Translate and solve using proportions: What percent of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c7bef200c216bbe8be23cd2a2c1371d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-124ad7404803de52a9cf2d7b24175956_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1491140\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1438795\">37.5%<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1491140\" data-type=\"solution\">\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1166498049771\" data-bullet-style=\"bullet\">\n<li><strong>Proportion<\/strong>\n<ul id=\"eip-id4505152\">\n<li>A proportion is an equation of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-956170b66c86da7bf9c392eca461afb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#99;&#125;&#123;&#100;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" style=\"vertical-align: -6px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1edd53778d94abb1dc1e19acff79e9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"40\" style=\"vertical-align: -4px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a75a5c231bda14b9edf71e02177f4b18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/>.The proportion states two ratios or rates are equal. The proportion is read \u201c<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>, as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> is to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4e8716946f6a868f015e0d62f28bc540_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/>\u201d.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Cross Products of a Proportion<\/strong>\n<ul id=\"eip-id1166665440339\">\n<li>For any proportion of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-956170b66c86da7bf9c392eca461afb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#99;&#125;&#123;&#100;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" style=\"vertical-align: -6px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1edd53778d94abb1dc1e19acff79e9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"40\" style=\"vertical-align: -4px;\" \/>, its cross products are equal: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bffd70f84246c57f11b860d87e6c7d82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#100;&#61;&#98;&#92;&#99;&#100;&#111;&#116;&#32;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"83\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Percent Proportion<\/strong>\n<ul id=\"eip-id1166625630839\">\n<li>The amount is to the base as the percent is to 100. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a2203f3a3e3ac4f1de287dbadb9cfb37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#109;&#111;&#117;&#110;&#116;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#97;&#115;&#101;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#101;&#114;&#99;&#101;&#110;&#116;&#125;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"118\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1166490867506\">\n<dt>proportion<\/dt>\n<dd id=\"fs-id1166490867511\">A proportion is an equation of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-956170b66c86da7bf9c392eca461afb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#99;&#125;&#123;&#100;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" style=\"vertical-align: -6px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1edd53778d94abb1dc1e19acff79e9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"40\" style=\"vertical-align: -4px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a75a5c231bda14b9edf71e02177f4b18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/>.The proportion states two ratios or rates are equal. The proportion is read \u201c<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>, as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> is to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4e8716946f6a868f015e0d62f28bc540_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/>\u201d.<\/dd>\n<\/dl>\n<\/div>\n<h1 data-type=\"title\">6.3 Exercise Set<\/h1>\n<p id=\"eip-388\">In the following exercises, write each sentence as a proportion.<\/p>\n<ol class=\"twocolumn\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> is to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dce5a8d8a80b6aa9c2a9f6810851e582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> is to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3ce84e5db7a21ede193ebc490f03d2cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"25\" style=\"vertical-align: -1px;\" \/>.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> is to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-662f6ae8c8d225801ecf7f82bc73ef62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> is to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-89bc2c119dcafc9b555c6b2841530d2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/>.<\/li>\n<\/ol>\n<p id=\"fs-id1543474\">In the following exercises, determine whether each equation is a proportion.<\/p>\n<ol class=\"twocolumn\" start=\"3\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-710be68a9eaa176769aa05e9678ab0fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#54;&#125;&#123;&#49;&#50;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"62\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b309ea7407c401583e5937da67a9a86d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#54;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#49;&#125;&#123;&#49;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"55\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-993515c310954060c7412c537dcc0560_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#125;&#123;&#49;&#56;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#46;&#57;&#57;&#125;&#123;&#55;&#46;&#53;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"66\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-788af482cea8bc40e492cb99d9649de1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#51;&#46;&#53;&#125;&#123;&#56;&#46;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#49;&#46;&#48;&#53;&#125;&#123;&#49;&#57;&#46;&#53;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"84\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ol>\n<p id=\"eip-940\">In the following exercises, solve each proportion.<\/p>\n<ol class=\"twocolumn\" start=\"7\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a0edfffde78f27dc879454009b3f3d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#53;&#54;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fb505ad1d7bbb7bfd34e425955898b95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#57;&#125;&#123;&#54;&#51;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#122;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4fad5bc617f14f712b8ecc56e25a3876_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#97;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#53;&#125;&#123;&#49;&#49;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"56\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-65224e4e35e9d53bd6dc63b5e50d4f6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#56;&#125;&#123;&#49;&#53;&#52;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#55;&#125;&#123;&#112;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"66\" style=\"vertical-align: -9px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-79a7883a2a61d94f7c83c9f6e3821424_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#45;&#56;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#52;&#50;&#125;&#123;&#52;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"70\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1c05944aa3ccde6ea7bb171c20b43a48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#46;&#54;&#125;&#123;&#51;&#46;&#57;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#99;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"52\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8665157d1f85a3c515d5eee7cb3e581d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#46;&#55;&#125;&#123;&#106;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#46;&#57;&#125;&#123;&#48;&#46;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"63\" style=\"vertical-align: -9px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-70a5702ce75f855a50a33dd51e6c984b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#125;&#123;&#49;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#109;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"50\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ol>\n<p id=\"eip-371\">In the following exercises, solve the proportion problem.<\/p>\n<ol start=\"15\">\n<li>Pediatricians prescribe <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> millilitre s (ml) of acetaminophen for every <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dd40a7f142c1fc4152e724db5432f76b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> pounds of a child\u2019s weight. How many millilitres of acetaminophen will the doctor prescribe for Jocelyn, who weighs <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1a494309aca1bdc45eb593f8e8497226_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/> pounds?<\/li>\n<li>At the gym, Carol takes her pulse for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> sec and counts <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-23ae1c0b89342725f5c66b11294f8bcc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> beats. How many beats per minute is this? Has Carol met her target heart rate of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-234152ae1b4cdc9a3ed0c84de7768396_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> beats per minute?<\/li>\n<li>A new energy drink advertises <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-03117bb3f0bf7a2731ff40216b326a79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> calories for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> ounces. How many calories are in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> ounces of the drink?<\/li>\n<li>Karen eats <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b8fa03e1b526c6d07ec843385490ca4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> cup of oatmeal that counts for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> points on her weight loss program. Her husband, Joe, can have <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> points of oatmeal for breakfast. How much oatmeal can he have?<\/li>\n<li>Brianna, who weighs <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> kg, just received her shots and needs a pain killer. The pain killer is prescribed for children at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/> milligrams (mg) for every <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> kilogram (kg) of the child\u2019s weight. How many milligrams will the doctor prescribe?<\/li>\n<li>Kevin wants to keep his heart rate at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-21b40b26dcd5c46e571710b78f863a87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> beats per minute while training. During his workout he counts <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a7b50e6fd02515483149eb902ea18dfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> beats in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> seconds. How many beats per minute is this? Has Kevin met his target<\/li>\n<li>One brand of microwave popcorn has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-454fa4f8a22c90ab5a5245afd540f8f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> calories per serving. A whole bag of this popcorn has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a880aa3dee267fff1a375dd7cfcaa389_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> servings. How many calories are in a whole bag of this microwave popcorn?<\/li>\n<li>Marissa loves the Caramel Macchiato at the coffee shop. The <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8dde8d4cade60a4f3ca0e779512b974c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> oz. medium size has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-16041c37d4dd0e24a1f8c6347e689355_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: -1px;\" \/> calories. How many calories will she get if she drinks the large <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-930d01a5f622cee5952bab4752e56063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> oz. size?<\/li>\n<li>For every <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> kilogram (kg) of a child\u2019s weight, pediatricians prescribe <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/> milligrams (mg) of a fever reducer. If Isabella weighs <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> kg, how many milligrams of the fever reducer will the pediatrician prescribe?<\/li>\n<\/ol>\n<p id=\"eip-390\">In the following exercises, translate to a proportion.<\/p>\n<ol start=\"24\">\n<li>What number is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9678648ac08710f37fd6ec8463d22aa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#53;&#92;&#37;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"32\" style=\"vertical-align: -1px;\" \/> of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cfc1c93ce0328f593fef2ace92eb09b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#48;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"35\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1a494309aca1bdc45eb593f8e8497226_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-abae14b12dd0a7d759d40f3165c6de54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#48;&#92;&#37;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"32\" style=\"vertical-align: -1px;\" \/> of what number?<\/li>\n<li>What percent of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-93bab3e1e2449c9eb7d50303281fbada_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-04ed0f3c3ddec6185a814f68e6591933_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"25\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<p id=\"eip-773\">In the following exercises, translate and solve using proportions.<\/p>\n<ol start=\"27\">\n<li>What number is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9ac97cdc85e10b0d7071d846a43c4409_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#53;&#92;&#37;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"32\" style=\"vertical-align: -1px;\" \/> of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-80c7ce430fab60e63b9e2ace4265c324_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#48;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"34\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-672fc02068a035514f5977cbebfb1e05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#55;&#92;&#37;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"31\" style=\"vertical-align: -1px;\" \/> of what number is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9792cb88fc91ad2384a7ead6e5572420_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#55;&#46;&#54;&#53;&#125;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>What percent of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f0667d6d1eb4ec64cf031a4453d58121_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-babe24b60400a2cbb413570dd9f0e7fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"25\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<h1>Answers<\/h1>\n<ol class=\"twocolumn\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1aca54abc7166fc4e8940d8b9d0789fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#49;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#54;&#125;&#123;&#49;&#51;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"62\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-03557a371711d222d7d278f737d726f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#125;&#123;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#54;&#125;&#123;&#52;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"55\" style=\"vertical-align: -6px;\" \/><\/li>\n<li>yes<\/li>\n<li>no<\/li>\n<li>no<\/li>\n<li>yes<\/li>\n<li>49<\/li>\n<li>47<\/li>\n<li>9<\/li>\n<li>-11<\/li>\n<li>7<\/li>\n<li>2<\/li>\n<li>0.6<\/li>\n<li>14.4<\/li>\n<li>9 ml<\/li>\n<li>114, no<\/li>\n<li>159 cal<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-072be8a042b646904526f671ee717bc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#117;&#112;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/><\/li>\n<li>90 mg<\/li>\n<li>162, no<\/li>\n<li>420 cal<\/li>\n<li>300 cal<\/li>\n<li>180 mg<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d0fb2f78f2f1fc4582d60bf382e6fb70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#110;&#125;&#123;&#50;&#53;&#48;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#53;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"69\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ad1609bf5fd803a855511e9eaacc2441_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#53;&#125;&#123;&#110;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#48;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"62\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f177edcd3d1a70c12e67f176ab820b11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#55;&#125;&#123;&#56;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#112;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"62\" style=\"vertical-align: -7px;\" \/><\/li>\n<li>117<\/li>\n<li>45<\/li>\n<li>25%<\/li>\n<\/ol>\n<h1>Attributions<\/h1>\n<ol>\n<li>This chapter has been adapted from \u201cSolve Proportions and their Applications\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, 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.<\/li>\n<li><a href=\"https:\/\/pressbooks.oer.hawaii.edu\/humannutrition2\/chapter\/2-the-cardiovascular-system\/\">OER.hawaii.edu<\/a><\/li>\n<li>Wikipedia<\/li>\n<li>\u00a0Government of Canada Statistics<\/li>\n<\/ol>\n","protected":false},"author":125,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1669","chapter","type-chapter","status-publish","hentry"],"part":1441,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/1669","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/users\/125"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/1669\/revisions"}],"predecessor-version":[{"id":1670,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/1669\/revisions\/1670"}],"part":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/parts\/1441"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/1669\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/media?parent=1669"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapter-type?post=1669"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/contributor?post=1669"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/license?post=1669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}