{"id":1607,"date":"2019-07-29T13:13:24","date_gmt":"2019-07-29T17:13:24","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1607"},"modified":"2019-07-29T15:23:56","modified_gmt":"2019-07-29T19:23:56","slug":"answer-key-7-9","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-7-9\/","title":{"raw":"Answer Key 7.9","rendered":"Answer Key 7.9"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\begin{array}{rrl}\r\n\\\\\r\nR&=&J+10 \\\\\r\nR+4&=&2(J+4)\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\begin{array}{rrl}\r\n\\\\\r\nF&=&4S \\\\\r\nF+20&=&2(S+20)\r\n\\end{array}\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rrl}\r\n\\\\\r\nP&=&J+20 \\\\\r\nP+2&=&2(J+2)\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\begin{array}{rrl}\r\n\\\\\r\nD&=&23+A \\\\\r\nD+6&=&2(A+6)\r\n\\end{array}\\)<\/li>\r\n \t
  5. \\(\\begin{array}{rrl}\r\n\\\\\r\nF&=&B+4 \\\\\r\n(F-5)+(B-5)&=&48\r\n\\end{array}\\)<\/li>\r\n \t
  6. \\(\\begin{array}{rrl}\r\n\\\\\r\nJ&=&4M \\\\\r\n(J-5)+(M-5)&=&50\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\begin{array}{rrl}\r\n\\\\\r\nT&=&5+J \\\\\r\n(T+6)+(J+6)&=&79\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\(\\begin{array}{rrl}\r\n\\\\\r\nJ&=&2L \\\\\r\n(J+3)+(L+3)&=&54\r\n\\end{array}\\)<\/li>\r\n \t
  9. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&J&+&m&=&32&& \\\\\r\n&&&-&m&&-m&& \\\\\r\n\\midrule\r\n&&&&J&=&32&-&m \\\\ \\\\\r\n&&J&-&4&=&2(m&-&4) \\\\\r\n(32&-&m)&-&4&=&2m&-&8 \\\\\r\n32&-&m&-&4&=&2m&-&8 \\\\\r\n&&28&-&m&=&2m&-&8 \\\\\r\n&&+8&+&m&&+m&+&8 \\\\\r\n\\midrule\r\n&&&&\\dfrac{36}{3}&=&\\dfrac{3m}{3}&& \\\\ \\\\\r\n&&&&m&=&12&& \\\\ \\\\\r\n&&&&\\therefore J&=&32&-&m \\\\\r\n&&&&J&=&32&-&12 \\\\\r\n&&&&J&=&20&&\r\n\\end{array}\\)<\/li>\r\n \t
  10. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&F&+&S&=&56&& \\\\\r\n&&&-&S&=&&-&S \\\\\r\n\\midrule\r\n&&&&F&=&56&-&S \\\\ \\\\\r\n&&F&-&4&=&3(S&-&4) \\\\\r\n56&-&S&-&4&=&3S&-&12 \\\\\r\n&+&S&+&12&&+S&+&12 \\\\\r\n\\midrule\r\n&&&&\\dfrac{64}{4}&=&\\dfrac{4S}{4}&& \\\\ \\\\\r\n&&&&S&=&16&& \\\\ \\\\\r\n&&&&\\therefore F&=&56&-&S \\\\\r\n&&&&F&=&56&-&16 \\\\\r\n&&&&F&=&40&&\r\n\\end{array}\\)<\/li>\r\n \t
  11. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrrl}\r\n\\\\\r\n&&w&+&B&=&20&&& \\\\\r\n&&-w&&&&&-&w& \\\\\r\n\\midrule\r\n&&&&B&=&20&-&w& \\\\ \\\\\r\n&&B&-&4&=&\\dfrac{1}{2}(w&-&4)& \\\\ \\\\\r\n20&-&w&-&4&=&\\dfrac{1}{2}(w&-&4)& \\\\ \\\\\r\n&&[16&-&w&=&\\dfrac{1}{2}(w&-&4)]&(2) \\\\\r\n\\end{array}\r\n&\r\n\\begin{array}{rrrrrrr}\r\n32&-&2w&=&w&-&4 \\\\\r\n+4&+&2w&&+2w&+&4 \\\\\r\n\\midrule\r\n&&\\dfrac{36}{3}&=&\\dfrac{3w}{3}&& \\\\ \\\\\r\n&&w&=&12&& \\\\ \\\\\r\n&&B&=&20&-&w \\\\\r\n&&B&=&20&-&12 \\\\\r\n&&B&=&8&&\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\begin{array}{rrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&m&=&36&& \\\\\r\n&&D&=&3&& \\\\ \\\\\r\nm&+&x&=&4(D&+&x) \\\\\r\n36&+&x&=&4(3&+&x) \\\\\r\n36&+&x&=&12&+&4x \\\\\r\n-12&-&x&&-12&-&x \\\\\r\n\\midrule\r\n&&\\dfrac{24}{3}&=&\\dfrac{3x}{3}&& \\\\ \\\\\r\n&&x&=&8&&\\text{ years} \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\begin{array}{rrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&B_\\text{o}&=&2B_\\text{y}&& \\\\ \\\\\r\nB_\\text{o}&-&5&=&\\phantom{-}3(B_\\text{y}&-&5) \\\\\r\n2B_\\text{y}&-&5&=&\\phantom{-}3B_\\text{y}&-&15 \\\\\r\n-3B_\\text{y}&+&5&&-3B_\\text{y}&+&5 \\\\\r\n\\midrule\r\n&&-B_\\text{y}&=&-10&& \\\\\r\n&&B_\\text{y}&=&\\phantom{-}10&& \\\\ \\\\\r\n&&\\therefore B_\\text{o}&=&2B_\\text{y}&& \\\\\r\n&&B_\\text{o}&=&2(10)&& \\\\\r\n&&B_\\text{o}&=&20&&\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&P&=&30&& \\\\\r\n&&V&=&22&& \\\\ \\\\\r\nP&-&x&=&2(V&-&x) \\\\\r\n30&-&x&=&2(22&-&x) \\\\\r\n30&-&x&=&44&-&2x \\\\\r\n-44&+&x&&-44&+&x \\\\\r\n\\midrule\r\n&&-14&=&-x&& \\\\\r\n&&x&=&14&&\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&&&m&=&2c \\\\ \\\\\r\n(m&-&7)&+&(c&-&7)&=&13 \\\\\r\n&&m&+&c&-&14&=&13 \\\\\r\n&&2c&+&c&-&14&=&13 \\\\\r\n&&&&&+&14&&+14 \\\\\r\n\\midrule\r\n&&&&&&\\dfrac{3c}{3}&=&\\dfrac{27}{3} \\\\ \\\\\r\n&&&&&&c&=&9 \\\\ \\\\\r\n&&&&&&\\therefore m&=&2c \\\\\r\n&&&&&&m&=&2(9) \\\\\r\n&&&&&&m&=&18\r\n\\end{array}\\)<\/li>\r\n \t
  16. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&J&+&m&=&35&& \\\\\r\n&&&-&m&&&-&m \\\\\r\n\\midrule\r\n&&&&J&=&35&-&m \\\\ \\\\\r\n&&J&-&10&=&2(m&-&10) \\\\\r\n35&-&m&-&10&=&2m&-&20 \\\\\r\n&&25&-&m&=&2m&-&20 \\\\\r\n&&-25&-&2m&&-2m&-&25 \\\\\r\n\\midrule\r\n&&&&-3m&=&-45&& \\\\ \\\\\r\n&&&&m&=&\\dfrac{-45}{-3}&\\text{or}&15 \\\\ \\\\\r\n&&&&\\therefore J&=&35&-&m \\\\\r\n&&&&J&=&35&-&15 \\\\\r\n&&&&J&=&20&&\r\n\\end{array}\\)<\/li>\r\n \t
  17. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&S&=&28&+&B \\\\ \\\\\r\n&&S&+&6&=&2(B&+&6) \\\\\r\n28&+&B&+&6&=&2B&+&12 \\\\\r\n&&B&+&34&=&2B&+&12 \\\\\r\n&&-B&-&12&=&-B&-&12 \\\\\r\n\\midrule\r\n&&&&22&=&B&& \\\\ \\\\\r\n&&&&S&=&28&+&B \\\\\r\n&&&&S&=&28&+&22 \\\\\r\n&&&&S&=&50&&\r\n\\end{array}\\)<\/li>\r\n \t
  18. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&c&+&w&=&64&& \\\\\r\n&&-c&&&&&-&c \\\\\r\n\\midrule\r\n&&&&w&=&64&-&c \\\\\r\n&&&&w&=&64&-&14 \\\\\r\n&&&&\\therefore w&=&50&& \\\\ \\\\\r\n&&w&+&4&=&3(c&+&4) \\\\\r\n64&-&c&+&4&=&3c&+&12 \\\\\r\n&+&c&-&12&&+c&-&12 \\\\\r\n\\midrule\r\n&&&&\\dfrac{56}{4}&=&\\dfrac{4c}{4}&& \\\\ \\\\\r\n&&&&c&=&14&&\r\n\\end{array}\\)<\/li>\r\n \t
  19. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&S&=&12&& \\\\\r\n&&T&=&36&& \\\\ \\\\\r\nT&+&x&=&2(S&+&x) \\\\\r\n36&+&x&=&2(12&+&x) \\\\\r\n36&+&x&=&24&+&2x \\\\\r\n-24&-&x&&-24&-&x \\\\\r\n\\midrule\r\n&&x&=&12&&\r\n\\end{array}\\)<\/li>\r\n \t
  20. \\(\\begin{array}{rrrrrrrrrrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&&&&&&&F&=&3S&& \\\\\r\n&&&&&&&&&&D&=&S&-&3 \\\\ \\\\\r\nF&-&3&+&D&-&3&+&S&-&3&=&63&& \\\\\r\nF&&&+&D&&&+&S&-&9&=&63&& \\\\\r\n3S&&&+&S&-&3&+&S&-&9&=&63&& \\\\\r\n&&&&&&&&5S&-&12&=&63&& \\\\\r\n&&&&&&&&&+&12&&+12&& \\\\\r\n\\midrule\r\n&&&&&&&&&&\\dfrac{5S}{5}&=&\\dfrac{75}{5}&& \\\\ \\\\\r\n&&&&&&&&&&S&=&15&& \\\\ \\\\\r\n&&&&&&&&&&F&=&3S&& \\\\\r\n&&&&&&&&&&F&=&3(15)&\\text{or}&45 \\\\ \\\\\r\n&&&&&&&&&&D&=&S&-&3 \\\\\r\n&&&&&&&&&&D&=&15&-&3\\text{ or }12\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
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