Answer Key 7.9

$\begin{array}{rrl} \\ R&=&J+10 \\ R+4&=&2(J+4) \end{array}$
$\begin{array}{rrl} \\ F&=&4S \\ F+20&=&2(S+20) \end{array}$
$\begin{array}{rrl} \\ P&=&J+20 \\ P+2&=&2(J+2) \end{array}$
$\begin{array}{rrl} \\ D&=&23+A \\ D+6&=&2(A+6) \end{array}$
$\begin{array}{rrl} \\ F&=&B+4 \\ (F-5)+(B-5)&=&48 \end{array}$
$\begin{array}{rrl} \\ J&=&4M \\ (J-5)+(M-5)&=&50 \end{array}$
$\begin{array}{rrl} \\ T&=&5+J \\ (T+6)+(J+6)&=&79 \end{array}$
$\begin{array}{rrl} \\ J&=&2L \\ (J+3)+(L+3)&=&54 \end{array}$
$\begin{array}{rrrrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &&J&+&m&=&32&& \\ &&&-&m&&-m&& \\ \midrule &&&&J&=&32&-&m \\ \\ &&J&-&4&=&2(m&-&4) \\ (32&-&m)&-&4&=&2m&-&8 \\ 32&-&m&-&4&=&2m&-&8 \\ &&28&-&m&=&2m&-&8 \\ &&+8&+&m&&+m&+&8 \\ \midrule &&&&\dfrac{36}{3}&=&\dfrac{3m}{3}&& \\ \\ &&&&m&=&12&& \\ \\ &&&&\therefore J&=&32&-&m \\ &&&&J&=&32&-&12 \\ &&&&J&=&20&& \end{array}$
$\begin{array}{rrrrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &&F&+&S&=&56&& \\ &&&-&S&=&&-&S \\ \midrule &&&&F&=&56&-&S \\ \\ &&F&-&4&=&3(S&-&4) \\ 56&-&S&-&4&=&3S&-&12 \\ &+&S&+&12&&+S&+&12 \\ \midrule &&&&\dfrac{64}{4}&=&\dfrac{4S}{4}&& \\ \\ &&&&S&=&16&& \\ \\ &&&&\therefore F&=&56&-&S \\ &&&&F&=&56&-&16 \\ &&&&F&=&40&& \end{array}$
$\begin{array}{rr} \\ \\ \\ \\ \\ \begin{array}{rrrrrrrrrl} \\ &&w&+&B&=&20&&& \\ &&-w&&&&&-&w& \\ \midrule &&&&B&=&20&-&w& \\ \\ &&B&-&4&=&\dfrac{1}{2}(w&-&4)& \\ \\ 20&-&w&-&4&=&\dfrac{1}{2}(w&-&4)& \\ \\ &&[16&-&w&=&\dfrac{1}{2}(w&-&4)]&(2) \\ \end{array} & \begin{array}{rrrrrrr} 32&-&2w&=&w&-&4 \\ +4&+&2w&&+2w&+&4 \\ \midrule &&\dfrac{36}{3}&=&\dfrac{3w}{3}&& \\ \\ &&w&=&12&& \\ \\ &&B&=&20&-&w \\ &&B&=&20&-&12 \\ &&B&=&8&& \end{array} \end{array}$
$\begin{array}{rrrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &&m&=&36&& \\ &&D&=&3&& \\ \\ m&+&x&=&4(D&+&x) \\ 36&+&x&=&4(3&+&x) \\ 36&+&x&=&12&+&4x \\ -12&-&x&&-12&-&x \\ \midrule &&\dfrac{24}{3}&=&\dfrac{3x}{3}&& \\ \\ &&x&=&8&&\text{ years} \\ \end{array}$
$\begin{array}{rrrrlrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &&B_\text{o}&=&2B_\text{y}&& \\ \\ B_\text{o}&-&5&=&\phantom{-}3(B_\text{y}&-&5) \\ 2B_\text{y}&-&5&=&\phantom{-}3B_\text{y}&-&15 \\ -3B_\text{y}&+&5&&-3B_\text{y}&+&5 \\ \midrule &&-B_\text{y}&=&-10&& \\ &&B_\text{y}&=&\phantom{-}10&& \\ \\ &&\therefore B_\text{o}&=&2B_\text{y}&& \\ &&B_\text{o}&=&2(10)&& \\ &&B_\text{o}&=&20&& \end{array}$
$\begin{array}{rrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ &&P&=&30&& \\ &&V&=&22&& \\ \\ P&-&x&=&2(V&-&x) \\ 30&-&x&=&2(22&-&x) \\ 30&-&x&=&44&-&2x \\ -44&+&x&&-44&+&x \\ \midrule &&-14&=&-x&& \\ &&x&=&14&& \end{array}$
$\begin{array}{rrrrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &&&&&&m&=&2c \\ \\ (m&-&7)&+&(c&-&7)&=&13 \\ &&m&+&c&-&14&=&13 \\ &&2c&+&c&-&14&=&13 \\ &&&&&+&14&&+14 \\ \midrule &&&&&&\dfrac{3c}{3}&=&\dfrac{27}{3} \\ \\ &&&&&&c&=&9 \\ \\ &&&&&&\therefore m&=&2c \\ &&&&&&m&=&2(9) \\ &&&&&&m&=&18 \end{array}$
$\begin{array}{rrrrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &&J&+&m&=&35&& \\ &&&-&m&&&-&m \\ \midrule &&&&J&=&35&-&m \\ \\ &&J&-&10&=&2(m&-&10) \\ 35&-&m&-&10&=&2m&-&20 \\ &&25&-&m&=&2m&-&20 \\ &&-25&-&2m&&-2m&-&25 \\ \midrule &&&&-3m&=&-45&& \\ \\ &&&&m&=&\dfrac{-45}{-3}&\text{or}&15 \\ \\ &&&&\therefore J&=&35&-&m \\ &&&&J&=&35&-&15 \\ &&&&J&=&20&& \end{array}$
$\begin{array}{rrrrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &&&&S&=&28&+&B \\ \\ &&S&+&6&=&2(B&+&6) \\ 28&+&B&+&6&=&2B&+&12 \\ &&B&+&34&=&2B&+&12 \\ &&-B&-&12&=&-B&-&12 \\ \midrule &&&&22&=&B&& \\ \\ &&&&S&=&28&+&B \\ &&&&S&=&28&+&22 \\ &&&&S&=&50&& \end{array}$
$\begin{array}{rrrrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &&c&+&w&=&64&& \\ &&-c&&&&&-&c \\ \midrule &&&&w&=&64&-&c \\ &&&&w&=&64&-&14 \\ &&&&\therefore w&=&50&& \\ \\ &&w&+&4&=&3(c&+&4) \\ 64&-&c&+&4&=&3c&+&12 \\ &+&c&-&12&&+c&-&12 \\ \midrule &&&&\dfrac{56}{4}&=&\dfrac{4c}{4}&& \\ \\ &&&&c&=&14&& \end{array}$
$\begin{array}{rrrrrrr} \\ \\ \\ \\ \\ \\ \\ &&S&=&12&& \\ &&T&=&36&& \\ \\ T&+&x&=&2(S&+&x) \\ 36&+&x&=&2(12&+&x) \\ 36&+&x&=&24&+&2x \\ -24&-&x&&-24&-&x \\ \midrule &&x&=&12&& \end{array}$
$\begin{array}{rrrrrrrrrrrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &&&&&&&&&&F&=&3S&& \\ &&&&&&&&&&D&=&S&-&3 \\ \\ F&-&3&+&D&-&3&+&S&-&3&=&63&& \\ F&&&+&D&&&+&S&-&9&=&63&& \\ 3S&&&+&S&-&3&+&S&-&9&=&63&& \\ &&&&&&&&5S&-&12&=&63&& \\ &&&&&&&&&+&12&&+12&& \\ \midrule &&&&&&&&&&\dfrac{5S}{5}&=&\dfrac{75}{5}&& \\ \\ &&&&&&&&&&S&=&15&& \\ \\ &&&&&&&&&&F&=&3S&& \\ &&&&&&&&&&F&=&3(15)&\text{or}&45 \\ \\ &&&&&&&&&&D&=&S&-&3 \\ &&&&&&&&&&D&=&15&-&3\text{ or }12 \end{array}$

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