{"id":1911,"date":"2021-12-02T19:39:57","date_gmt":"2021-12-03T00:39:57","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-7-9\/"},"modified":"2022-11-02T10:38:21","modified_gmt":"2022-11-02T14:38:21","slug":"answer-key-7-9","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-7-9\/","title":{"raw":"Answer Key 7.9","rendered":"Answer Key 7.9"},"content":{"raw":"<ol>\n \t<li>[latex]\\begin{array}{rrl}\\\\\nR&amp;=&amp;J+10 \\\\\nR+4&amp;=&amp;2(J+4)\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\begin{array}{rrl}\\\\\nF&amp;=&amp;4S \\\\\nF+20&amp;=&amp;2(S+20)\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\begin{array}{rrl}\\\\\nP&amp;=&amp;J+20 \\\\\nP+2&amp;=&amp;2(J+2)\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\begin{array}{rrl}\\\\\nD&amp;=&amp;23+A \\\\\nD+6&amp;=&amp;2(A+6)\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\begin{array}{rrl}\\\\\nF&amp;=&amp;B+4 \\\\\n(F-5)+(B-5)&amp;=&amp;48\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\begin{array}{rrl}\\\\\nJ&amp;=&amp;4M \\\\\n(J-5)+(M-5)&amp;=&amp;50\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\begin{array}{rrl}\\\\\nT&amp;=&amp;5+J \\\\\n(T+6)+(J+6)&amp;=&amp;79\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\begin{array}{rrl}\\\\\nJ&amp;=&amp;2L \\\\\n(J+3)+(L+3)&amp;=&amp;54\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n&amp;&amp;J&amp;+&amp;m&amp;=&amp;32&amp;&amp; \\\\\n&amp;&amp;&amp;-&amp;m&amp;&amp;-m&amp;&amp; \\\\\n\\hline\n&amp;&amp;&amp;&amp;J&amp;=&amp;32&amp;-&amp;m \\\\ \\\\\n&amp;&amp;J&amp;-&amp;4&amp;=&amp;2(m&amp;-&amp;4) \\\\\n(32&amp;-&amp;m)&amp;-&amp;4&amp;=&amp;2m&amp;-&amp;8 \\\\\n32&amp;-&amp;m&amp;-&amp;4&amp;=&amp;2m&amp;-&amp;8 \\\\\n&amp;&amp;28&amp;-&amp;m&amp;=&amp;2m&amp;-&amp;8 \\\\\n&amp;&amp;+8&amp;+&amp;m&amp;&amp;+m&amp;+&amp;8 \\\\\n\\hline\n&amp;&amp;&amp;&amp;\\dfrac{36}{3}&amp;=&amp;\\dfrac{3m}{3}&amp;&amp; \\\\ \\\\\n&amp;&amp;&amp;&amp;m&amp;=&amp;12&amp;&amp; \\\\ \\\\\n&amp;&amp;&amp;&amp;\\therefore J&amp;=&amp;32&amp;-&amp;m \\\\\n&amp;&amp;&amp;&amp;J&amp;=&amp;32&amp;-&amp;12 \\\\\n&amp;&amp;&amp;&amp;J&amp;=&amp;20&amp;&amp;\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n&amp;&amp;F&amp;+&amp;S&amp;=&amp;56&amp;&amp; \\\\\n&amp;&amp;&amp;-&amp;S&amp;=&amp;&amp;-&amp;S \\\\\n\\hline\n&amp;&amp;&amp;&amp;F&amp;=&amp;56&amp;-&amp;S \\\\ \\\\\n&amp;&amp;F&amp;-&amp;4&amp;=&amp;3(S&amp;-&amp;4) \\\\\n56&amp;-&amp;S&amp;-&amp;4&amp;=&amp;3S&amp;-&amp;12 \\\\\n&amp;+&amp;S&amp;+&amp;12&amp;&amp;+S&amp;+&amp;12 \\\\\n\\hline\n&amp;&amp;&amp;&amp;\\dfrac{64}{4}&amp;=&amp;\\dfrac{4S}{4}&amp;&amp; \\\\ \\\\\n&amp;&amp;&amp;&amp;S&amp;=&amp;16&amp;&amp; \\\\ \\\\\n&amp;&amp;&amp;&amp;\\therefore F&amp;=&amp;56&amp;-&amp;S \\\\\n&amp;&amp;&amp;&amp;F&amp;=&amp;56&amp;-&amp;16 \\\\\n&amp;&amp;&amp;&amp;F&amp;=&amp;40&amp;&amp;\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rr}\n\\begin{array}[t]{rrrrrrrrrl}\n&amp;&amp;w&amp;+&amp;B&amp;=&amp;20&amp;&amp;&amp; \\\\\n&amp;&amp;-w&amp;&amp;&amp;&amp;&amp;-&amp;w&amp; \\\\\n\\hline\n&amp;&amp;&amp;&amp;B&amp;=&amp;20&amp;-&amp;w&amp; \\\\ \\\\\n&amp;&amp;B&amp;-&amp;4&amp;=&amp;\\dfrac{1}{2}(w&amp;-&amp;4)&amp; \\\\ \\\\\n20&amp;-&amp;w&amp;-&amp;4&amp;=&amp;\\dfrac{1}{2}(w&amp;-&amp;4)&amp; \\\\ \\\\\n&amp;&amp;[16&amp;-&amp;w&amp;=&amp;\\dfrac{1}{2}(w&amp;-&amp;4)]&amp;(2) \\\\\n\\end{array}\n&amp;\n\\begin{array}[t]{rrrrrrr}\n32&amp;-&amp;2w&amp;=&amp;w&amp;-&amp;4 \\\\\n+4&amp;+&amp;2w&amp;&amp;+2w&amp;+&amp;4 \\\\\n\\hline\n&amp;&amp;\\dfrac{36}{3}&amp;=&amp;\\dfrac{3w}{3}&amp;&amp; \\\\ \\\\\n&amp;&amp;w&amp;=&amp;12&amp;&amp; \\\\ \\\\\n&amp;&amp;B&amp;=&amp;20&amp;-&amp;w \\\\\n&amp;&amp;B&amp;=&amp;20&amp;-&amp;12 \\\\\n&amp;&amp;B&amp;=&amp;8&amp;&amp;\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrl}\n&amp;&amp;m&amp;=&amp;36&amp;&amp; \\\\\n&amp;&amp;D&amp;=&amp;3&amp;&amp; \\\\ \\\\\nm&amp;+&amp;x&amp;=&amp;4(D&amp;+&amp;x) \\\\\n36&amp;+&amp;x&amp;=&amp;4(3&amp;+&amp;x) \\\\\n36&amp;+&amp;x&amp;=&amp;12&amp;+&amp;4x \\\\\n-12&amp;-&amp;x&amp;&amp;-12&amp;-&amp;x \\\\\n\\hline\n&amp;&amp;\\dfrac{24}{3}&amp;=&amp;\\dfrac{3x}{3}&amp;&amp; \\\\ \\\\\n&amp;&amp;x&amp;=&amp;8&amp;&amp;\\text{ years} \\\\\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\n&amp;&amp;B_\\text{o}&amp;=&amp;2B_\\text{y}&amp;&amp; \\\\ \\\\\nB_\\text{o}&amp;-&amp;5&amp;=&amp;\\phantom{-}3(B_\\text{y}&amp;-&amp;5) \\\\\n2B_\\text{y}&amp;-&amp;5&amp;=&amp;\\phantom{-}3B_\\text{y}&amp;-&amp;15 \\\\\n-3B_\\text{y}&amp;+&amp;5&amp;&amp;-3B_\\text{y}&amp;+&amp;5 \\\\\n\\hline\n&amp;&amp;-B_\\text{y}&amp;=&amp;-10&amp;&amp; \\\\\n&amp;&amp;B_\\text{y}&amp;=&amp;\\phantom{-}10&amp;&amp; \\\\ \\\\\n&amp;&amp;\\therefore B_\\text{o}&amp;=&amp;2B_\\text{y}&amp;&amp; \\\\\n&amp;&amp;B_\\text{o}&amp;=&amp;2(10)&amp;&amp; \\\\\n&amp;&amp;B_\\text{o}&amp;=&amp;20&amp;&amp;\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n&amp;&amp;P&amp;=&amp;30&amp;&amp; \\\\\n&amp;&amp;V&amp;=&amp;22&amp;&amp; \\\\ \\\\\nP&amp;-&amp;x&amp;=&amp;2(V&amp;-&amp;x) \\\\\n30&amp;-&amp;x&amp;=&amp;2(22&amp;-&amp;x) \\\\\n30&amp;-&amp;x&amp;=&amp;44&amp;-&amp;2x \\\\\n-44&amp;+&amp;x&amp;&amp;-44&amp;+&amp;x \\\\\n\\hline\n&amp;&amp;-14&amp;=&amp;-x&amp;&amp; \\\\\n&amp;&amp;x&amp;=&amp;14&amp;&amp;\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n&amp;&amp;&amp;&amp;&amp;&amp;m&amp;=&amp;2c \\\\ \\\\\n(m&amp;-&amp;7)&amp;+&amp;(c&amp;-&amp;7)&amp;=&amp;13 \\\\\n&amp;&amp;m&amp;+&amp;c&amp;-&amp;14&amp;=&amp;13 \\\\\n&amp;&amp;2c&amp;+&amp;c&amp;-&amp;14&amp;=&amp;13 \\\\\n&amp;&amp;&amp;&amp;&amp;+&amp;14&amp;&amp;+14 \\\\\n\\hline\n&amp;&amp;&amp;&amp;&amp;&amp;\\dfrac{3c}{3}&amp;=&amp;\\dfrac{27}{3} \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;&amp;c&amp;=&amp;9 \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;&amp;\\therefore m&amp;=&amp;2c \\\\\n&amp;&amp;&amp;&amp;&amp;&amp;m&amp;=&amp;2(9) \\\\\n&amp;&amp;&amp;&amp;&amp;&amp;m&amp;=&amp;18\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n&amp;&amp;J&amp;+&amp;m&amp;=&amp;35&amp;&amp; \\\\\n&amp;&amp;&amp;-&amp;m&amp;&amp;&amp;-&amp;m \\\\\n\\hline\n&amp;&amp;&amp;&amp;J&amp;=&amp;35&amp;-&amp;m \\\\ \\\\\n&amp;&amp;J&amp;-&amp;10&amp;=&amp;2(m&amp;-&amp;10) \\\\\n35&amp;-&amp;m&amp;-&amp;10&amp;=&amp;2m&amp;-&amp;20 \\\\\n&amp;&amp;25&amp;-&amp;m&amp;=&amp;2m&amp;-&amp;20 \\\\\n&amp;&amp;-25&amp;-&amp;2m&amp;&amp;-2m&amp;-&amp;25 \\\\\n\\hline\n&amp;&amp;&amp;&amp;-3m&amp;=&amp;-45&amp;&amp; \\\\ \\\\\n&amp;&amp;&amp;&amp;m&amp;=&amp;\\dfrac{-45}{-3}&amp;\\text{or}&amp;15 \\\\ \\\\\n&amp;&amp;&amp;&amp;\\therefore J&amp;=&amp;35&amp;-&amp;m \\\\\n&amp;&amp;&amp;&amp;J&amp;=&amp;35&amp;-&amp;15 \\\\\n&amp;&amp;&amp;&amp;J&amp;=&amp;20&amp;&amp;\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n&amp;&amp;&amp;&amp;S&amp;=&amp;28&amp;+&amp;B \\\\ \\\\\n&amp;&amp;S&amp;+&amp;6&amp;=&amp;2(B&amp;+&amp;6) \\\\\n28&amp;+&amp;B&amp;+&amp;6&amp;=&amp;2B&amp;+&amp;12 \\\\\n&amp;&amp;B&amp;+&amp;34&amp;=&amp;2B&amp;+&amp;12 \\\\\n&amp;&amp;-B&amp;-&amp;12&amp;=&amp;-B&amp;-&amp;12 \\\\\n\\hline\n&amp;&amp;&amp;&amp;22&amp;=&amp;B&amp;&amp; \\\\ \\\\\n&amp;&amp;&amp;&amp;S&amp;=&amp;28&amp;+&amp;B \\\\\n&amp;&amp;&amp;&amp;S&amp;=&amp;28&amp;+&amp;22 \\\\\n&amp;&amp;&amp;&amp;S&amp;=&amp;50&amp;&amp;\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n&amp;&amp;c&amp;+&amp;w&amp;=&amp;64&amp;&amp; \\\\\n&amp;&amp;-c&amp;&amp;&amp;&amp;&amp;-&amp;c \\\\\n\\hline\n&amp;&amp;&amp;&amp;w&amp;=&amp;64&amp;-&amp;c \\\\\n&amp;&amp;&amp;&amp;w&amp;=&amp;64&amp;-&amp;14 \\\\\n&amp;&amp;&amp;&amp;\\therefore w&amp;=&amp;50&amp;&amp; \\\\ \\\\\n&amp;&amp;w&amp;+&amp;4&amp;=&amp;3(c&amp;+&amp;4) \\\\\n64&amp;-&amp;c&amp;+&amp;4&amp;=&amp;3c&amp;+&amp;12 \\\\\n&amp;+&amp;c&amp;-&amp;12&amp;&amp;+c&amp;-&amp;12 \\\\\n\\hline\n&amp;&amp;&amp;&amp;\\dfrac{56}{4}&amp;=&amp;\\dfrac{4c}{4}&amp;&amp; \\\\ \\\\\n&amp;&amp;&amp;&amp;c&amp;=&amp;14&amp;&amp;\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n&amp;&amp;S&amp;=&amp;12&amp;&amp; \\\\\n&amp;&amp;T&amp;=&amp;36&amp;&amp; \\\\ \\\\\nT&amp;+&amp;x&amp;=&amp;2(S&amp;+&amp;x) \\\\\n36&amp;+&amp;x&amp;=&amp;2(12&amp;+&amp;x) \\\\\n36&amp;+&amp;x&amp;=&amp;24&amp;+&amp;2x \\\\\n-24&amp;-&amp;x&amp;&amp;-24&amp;-&amp;x \\\\\n\\hline\n&amp;&amp;x&amp;=&amp;12&amp;&amp;\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrrrrrrl}\n&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;F&amp;=&amp;3S&amp;&amp; \\\\\n&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;D&amp;=&amp;S&amp;-&amp;3 \\\\ \\\\\nF&amp;-&amp;3&amp;+&amp;D&amp;-&amp;3&amp;+&amp;S&amp;-&amp;3&amp;=&amp;63&amp;&amp; \\\\\nF&amp;&amp;&amp;+&amp;D&amp;&amp;&amp;+&amp;S&amp;-&amp;9&amp;=&amp;63&amp;&amp; \\\\\n3S&amp;&amp;&amp;+&amp;S&amp;-&amp;3&amp;+&amp;S&amp;-&amp;9&amp;=&amp;63&amp;&amp; \\\\\n&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;5S&amp;-&amp;12&amp;=&amp;63&amp;&amp; \\\\\n&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;+&amp;12&amp;&amp;+12&amp;&amp; \\\\\n\\hline\n&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;\\dfrac{5S}{5}&amp;=&amp;\\dfrac{75}{5}&amp;&amp; \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;S&amp;=&amp;15&amp;&amp; \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;F&amp;=&amp;3S&amp;&amp; \\\\\n&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;F&amp;=&amp;3(15)&amp;\\text{or}&amp;45 \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;D&amp;=&amp;S&amp;-&amp;3 \\\\\n&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;D&amp;=&amp;15&amp;-&amp;3\\text{ or }12\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"<ol>\n<li>[latex]\\begin{array}{rrl}\\\\ R&=&J+10 \\\\ R+4&=&2(J+4) \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rrl}\\\\ F&=&4S \\\\ F+20&=&2(S+20) \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rrl}\\\\ P&=&J+20 \\\\ P+2&=&2(J+2) \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rrl}\\\\ D&=&23+A \\\\ D+6&=&2(A+6) \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rrl}\\\\ F&=&B+4 \\\\ (F-5)+(B-5)&=&48 \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rrl}\\\\ J&=&4M \\\\ (J-5)+(M-5)&=&50 \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rrl}\\\\ T&=&5+J \\\\ (T+6)+(J+6)&=&79 \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rrl}\\\\ J&=&2L \\\\ (J+3)+(L+3)&=&54 \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrrrr} &&J&+&m&=&32&& \\\\ &&&-&m&&-m&& \\\\ \\hline &&&&J&=&32&-&m \\\\ \\\\ &&J&-&4&=&2(m&-&4) \\\\ (32&-&m)&-&4&=&2m&-&8 \\\\ 32&-&m&-&4&=&2m&-&8 \\\\ &&28&-&m&=&2m&-&8 \\\\ &&+8&+&m&&+m&+&8 \\\\ \\hline &&&&\\dfrac{36}{3}&=&\\dfrac{3m}{3}&& \\\\ \\\\ &&&&m&=&12&& \\\\ \\\\ &&&&\\therefore J&=&32&-&m \\\\ &&&&J&=&32&-&12 \\\\ &&&&J&=&20&& \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrrrr} &&F&+&S&=&56&& \\\\ &&&-&S&=&&-&S \\\\ \\hline &&&&F&=&56&-&S \\\\ \\\\ &&F&-&4&=&3(S&-&4) \\\\ 56&-&S&-&4&=&3S&-&12 \\\\ &+&S&+&12&&+S&+&12 \\\\ \\hline &&&&\\dfrac{64}{4}&=&\\dfrac{4S}{4}&& \\\\ \\\\ &&&&S&=&16&& \\\\ \\\\ &&&&\\therefore F&=&56&-&S \\\\ &&&&F&=&56&-&16 \\\\ &&&&F&=&40&& \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rr} \\begin{array}[t]{rrrrrrrrrl} &&w&+&B&=&20&&& \\\\ &&-w&&&&&-&w& \\\\ \\hline &&&&B&=&20&-&w& \\\\ \\\\ &&B&-&4&=&\\dfrac{1}{2}(w&-&4)& \\\\ \\\\ 20&-&w&-&4&=&\\dfrac{1}{2}(w&-&4)& \\\\ \\\\ &&[16&-&w&=&\\dfrac{1}{2}(w&-&4)]&(2) \\\\ \\end{array} & \\begin{array}[t]{rrrrrrr} 32&-&2w&=&w&-&4 \\\\ +4&+&2w&&+2w&+&4 \\\\ \\hline &&\\dfrac{36}{3}&=&\\dfrac{3w}{3}&& \\\\ \\\\ &&w&=&12&& \\\\ \\\\ &&B&=&20&-&w \\\\ &&B&=&20&-&12 \\\\ &&B&=&8&& \\end{array} \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrl} &&m&=&36&& \\\\ &&D&=&3&& \\\\ \\\\ m&+&x&=&4(D&+&x) \\\\ 36&+&x&=&4(3&+&x) \\\\ 36&+&x&=&12&+&4x \\\\ -12&-&x&&-12&-&x \\\\ \\hline &&\\dfrac{24}{3}&=&\\dfrac{3x}{3}&& \\\\ \\\\ &&x&=&8&&\\text{ years} \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrlrr} &&B_\\text{o}&=&2B_\\text{y}&& \\\\ \\\\ B_\\text{o}&-&5&=&\\phantom{-}3(B_\\text{y}&-&5) \\\\ 2B_\\text{y}&-&5&=&\\phantom{-}3B_\\text{y}&-&15 \\\\ -3B_\\text{y}&+&5&&-3B_\\text{y}&+&5 \\\\ \\hline &&-B_\\text{y}&=&-10&& \\\\ &&B_\\text{y}&=&\\phantom{-}10&& \\\\ \\\\ &&\\therefore B_\\text{o}&=&2B_\\text{y}&& \\\\ &&B_\\text{o}&=&2(10)&& \\\\ &&B_\\text{o}&=&20&& \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrr} &&P&=&30&& \\\\ &&V&=&22&& \\\\ \\\\ P&-&x&=&2(V&-&x) \\\\ 30&-&x&=&2(22&-&x) \\\\ 30&-&x&=&44&-&2x \\\\ -44&+&x&&-44&+&x \\\\ \\hline &&-14&=&-x&& \\\\ &&x&=&14&& \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrrrr} &&&&&&m&=&2c \\\\ \\\\ (m&-&7)&+&(c&-&7)&=&13 \\\\ &&m&+&c&-&14&=&13 \\\\ &&2c&+&c&-&14&=&13 \\\\ &&&&&+&14&&+14 \\\\ \\hline &&&&&&\\dfrac{3c}{3}&=&\\dfrac{27}{3} \\\\ \\\\ &&&&&&c&=&9 \\\\ \\\\ &&&&&&\\therefore m&=&2c \\\\ &&&&&&m&=&2(9) \\\\ &&&&&&m&=&18 \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrrrr} &&J&+&m&=&35&& \\\\ &&&-&m&&&-&m \\\\ \\hline &&&&J&=&35&-&m \\\\ \\\\ &&J&-&10&=&2(m&-&10) \\\\ 35&-&m&-&10&=&2m&-&20 \\\\ &&25&-&m&=&2m&-&20 \\\\ &&-25&-&2m&&-2m&-&25 \\\\ \\hline &&&&-3m&=&-45&& \\\\ \\\\ &&&&m&=&\\dfrac{-45}{-3}&\\text{or}&15 \\\\ \\\\ &&&&\\therefore J&=&35&-&m \\\\ &&&&J&=&35&-&15 \\\\ &&&&J&=&20&& \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrrrr} &&&&S&=&28&+&B \\\\ \\\\ &&S&+&6&=&2(B&+&6) \\\\ 28&+&B&+&6&=&2B&+&12 \\\\ &&B&+&34&=&2B&+&12 \\\\ &&-B&-&12&=&-B&-&12 \\\\ \\hline &&&&22&=&B&& \\\\ \\\\ &&&&S&=&28&+&B \\\\ &&&&S&=&28&+&22 \\\\ &&&&S&=&50&& \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrrrr} &&c&+&w&=&64&& \\\\ &&-c&&&&&-&c \\\\ \\hline &&&&w&=&64&-&c \\\\ &&&&w&=&64&-&14 \\\\ &&&&\\therefore w&=&50&& \\\\ \\\\ &&w&+&4&=&3(c&+&4) \\\\ 64&-&c&+&4&=&3c&+&12 \\\\ &+&c&-&12&&+c&-&12 \\\\ \\hline &&&&\\dfrac{56}{4}&=&\\dfrac{4c}{4}&& \\\\ \\\\ &&&&c&=&14&& \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrr} &&S&=&12&& \\\\ &&T&=&36&& \\\\ \\\\ T&+&x&=&2(S&+&x) \\\\ 36&+&x&=&2(12&+&x) \\\\ 36&+&x&=&24&+&2x \\\\ -24&-&x&&-24&-&x \\\\ \\hline &&x&=&12&& \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrrrrrrrrrl} &&&&&&&&&&F&=&3S&& \\\\ &&&&&&&&&&D&=&S&-&3 \\\\ \\\\ F&-&3&+&D&-&3&+&S&-&3&=&63&& \\\\ F&&&+&D&&&+&S&-&9&=&63&& \\\\ 3S&&&+&S&-&3&+&S&-&9&=&63&& \\\\ &&&&&&&&5S&-&12&=&63&& \\\\ &&&&&&&&&+&12&&+12&& \\\\ \\hline &&&&&&&&&&\\dfrac{5S}{5}&=&\\dfrac{75}{5}&& \\\\ \\\\ &&&&&&&&&&S&=&15&& \\\\ \\\\ &&&&&&&&&&F&=&3S&& \\\\ &&&&&&&&&&F&=&3(15)&\\text{or}&45 \\\\ \\\\ &&&&&&&&&&D&=&S&-&3 \\\\ &&&&&&&&&&D&=&15&-&3\\text{ or }12 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