Answer Key 5.5

  1. \left\{ \begin{array}{rrrrr} d&+&q&=&103 \\ 10d&+&25q&=&1525 \end{array} \right.
  2. \left\{ \begin{array}{rrrrr} n&+&f&=&34 \\ 5n&+&50f&=&1340 \end{array} \right.
  3. \left\{ \begin{array}{rrrrr} A&+&C&=&578 \\ 2A&+&1.5C&=&985 \end{array} \right.
  4. \left\{ \begin{array}{rrrrr} d&+&q&=&21 \\ 10d&+&25q&=&390 \end{array} \right.
  5. \left\{ \begin{array}{rrrrr} 5n&+&10d&=&225 \\ &&d&=&2n \end{array} \right.
  6. \left\{ \begin{array}{rrrrrrr} 25q&+&50f&=&375&& \\ &&q&=&f&+&3 \end{array} \right.
  7. \left\{ \begin{array}{rrrrr} I_{9.5}&+&I_{11}&=&10000\phantom{.00} \\ 0.095I_{9.5}&+&0.11I_{11}&=&1038.50 \end{array} \right.
  8. 7000(r)+9000(r+0.02)=900
  9. 1600(r)+2400(2r)=256
  10. 3000(r)+4500(r-0.02)=435
  11. \begin{array}{rrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &N&+&C&=&203 \\ &2N&+&1.25C&=&310 \\ \\ &(N&+&C&=&\phantom{-}203)(-2) \\ &-2N&-&2.00C&=&-406 \\ +&2N&+&1.25C&=&\phantom{-}310 \\ \midrule &&&\dfrac{-0.75C}{-0.75}&=&\dfrac{-96}{-0.75} \\ \\ &&&C&=&128 \\ \\ &&&N&=&203-C \\ &&&N&=&203-128 \\ &&&N&=&75 \end{array}
  12. \begin{array}{rrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &d&+&b&=&131 \\ &2.50d&+&2.75b&=&342 \\ \\ &(d&+&b&=&131)(-2.5) \\ &-2.50d&-&2.50b&=&-327.5 \\ +&2.50d&+&2.75b&=&\phantom{-}342 \\ \midrule &&&\dfrac{0.25b}{0.25}&=&\dfrac{14.5}{0.25} \\ \\ &&&b&=&58 \\ \\ &&&d&=&131-b \\ &&&d&=&131-58 \\ &&&d&=&73 \end{array}
  13. \begin{array}{rrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &d&+&q&=&\phantom{0}27 \\ &10d&+&25q&=&495 \\ \\ &(d&+&q&=&\phantom{-0}27)(-10) \\ &-10d&-&10q&=&-270 \\ +&10d&+&25q&=&\phantom{-}495 \\ \midrule &&&\dfrac{15q}{15}&=&\dfrac{225}{15} \\ \\ &&&q&=&15 \\ \\ &&&d&=&27-q \\ &&&d&=&27-15 \\ &&&d&=&12 \end{array}
  14. \begin{array}{rrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &d&+&n&=&18 \\ &10d&+&5n&=&115 \\ \\ &(d&+&n&=&18)(-5) \\ &-5d&-&5n&=&-90 \\ +&10d&+&5n&=&115 \\ \midrule &&&\dfrac{5d}{5}&=&\dfrac{25}{5} \\ \\ &&&d&=&5 \\ \\ &&&n&=&18-d \\ &&&n&=&18-5 \\ &&&n&=&13 \end{array}
  15. \begin{array}{rrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &S_{25}&+&S_{20}&=&\phantom{0}40 \\ &25S_{25}&+&20S_{20}&=&960 \\ \\ &(S_{25}&+&S_{20}&=&40)(-20) \\ &-20S_{25}&-&20S_{20}&=&-800 \\ +&25S_{25}&+&20S_{20}&=&\phantom{-}960 \\ \midrule &&&\dfrac{5S_{25}}{5}&=&\dfrac{160}{5} \\ \\ &&&S_{25}&=&32 \\ \\ &&&S_{20}&=&40-S_{25} \\ &&&S_{20}&=&40-32 \\ &&&S_{20}&=&8 \end{array}
  16. \begin{array}{rrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &S_{15}&+&S_{25}&=&\phantom{0}15 \\ &15S_{15}&+&25S_{25}&=&315 \\ \\ &(S_{15}&+&S_{25}&=&15)(-15) \\ &-15S_{15}&-&15S_{25}&=&-225 \\ +&15S_{15}&+&25S_{25}&=&\phantom{-}315 \\ \midrule &&&\dfrac{10S_{25}}{10}&=&\dfrac{90}{10} \\ \\ &&&S_{25}&=&9 \\ \\ &&&S_{15}&=&15-S_{25} \\ &&&S_{15}&=&15-9 \\ &&&S_{15}&=&6 \end{array}
  17. \begin{array}{rrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &I_{12}&+&I_{13}&=&27000 \\ &0.12I_{12}&+&0.13I_{13}&=&\phantom{0}3385 \\ \\ &(I_{12}&+&I_{13}&=&27000)(-0.12) \\ &-0.12I_{12}&-&0.12I_{13}&=&-3240 \\ +&0.12I_{12}&+&0.13I_{13}&=&\phantom{-}3385 \\ \midrule &&&\dfrac{0.01I_{13}}{0.01}&=&\dfrac{145}{0.01} \\ \\ &&&I_{13}&=&14500 \\ \\ &&&I_{12}&=&27000-I_{13} \\ &&&I_{12}&=&27000-14500 \\ &&&I_{12}&=&12500 \end{array}
  18. \begin{array}{rrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &I_5&+&I_{7.5}&=&50000 \\ &0.05I_5&+&0.075I_{7.5}&=&3250 \\ \\ &(I_5&+&I_{7.5}&=&50000)(-0.05) \\ &-0.05I_5&-&0.05I_{7.5}&=&-2500 \\ +&0.05I_5&+&0.075I_{7.5}&=&\phantom{-}3250 \\ \midrule &&&\dfrac{0.025I_{7.5}}{0.025}&=&\dfrac{750}{0.025} \\ \\ &&&I_{7.5}&=&30000 \\ \\ &&&I_5&=&50000-I_{7.5} \\ &&&I_5&=&50000-30000 \\ &&&I_5&=&20000 \end{array}
  19. \begin{array}{rrrrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &&10d&+&25q&=&605&& \\ &&&&d&=&q&-&6 \\ \\ 10(q&-&6)&+&25q&=&605&& \\ 10q&-&60&+&25q&=&605&& \\ &+&60&&&&+60&& \\ \midrule &&&&\dfrac{35q}{35}&=&\dfrac{665}{35}&& \\ \\ &&&&q&=&19&& \\ \\ &&&&d&=&q&-&6 \\ &&&&d&=&19&-&6 \\ &&&&d&=&13&& \\ \end{array}
  20. \begin{array}{rrrrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &&5n&+&10d&=&275&& \\ &&&&d&=&2n&-&10 \\ \\ 5n&+&10(2n&-&10)&=&275&& \\ 5n&+&20n&-&100&=&275&& \\ &&&+&100&&+100&& \\ \midrule &&&&\dfrac{25n}{25}&=&\dfrac{375}{25}&& \\ \\ &&&&n&=&15&& \\ \\ &&&&d&=&2n&-&10 \\ &&&&d&=&2(15)&-&10 \\ &&&&d&=&30&-&10 \\ &&&&d&=&20&& \end{array}
  21. \begin{array}{rrrrrrl} \\ \\ \\ \\ \\ \\ \\ 3000r&+&24000(r&-&0.04)&=&2010 \\ 3000r&+&24000r&-&960&=&2010 \\ &&&+&960&&+960 \\ \midrule &&&&\dfrac{27000r}{27000}&=&\dfrac{2970}{27000} \\ \\ &&&&r&=&0.11=11\% \\ &&0.11&-&0.04&=&0.07=7\% \\ \end{array}
  22. \begin{array}{rrrrcrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ 5000r&+&11000\left(\dfrac{2}{3}r\right)&=&1480&& \\ \\ 5000r&+&7333.33r&=&1480&& \\ \\ &&\dfrac{12333.33r}{12333.33}&=&\dfrac{1480}{12333.33}&& \\ \\ &&r&=&0.12&=&12\% \\ \\ &&\dfrac{2}{3}r&=&0.08&=&8\% \end{array}
  23. \begin{array}{rrrrrrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &&5n&+&10d&+&25q&=&510&& \\ &&&&&&n&=&2d&& \\ &&&&&&q&=&d&-&3 \\ \\ 5(2d)&+&10d&+&25(d&-&3)&=&510&& \\ 10d&+&10d&+&25d&-&75&=&510&& \\ &&&&&+&75&&+75&& \\ \midrule &&&&&&\dfrac{45d}{45}&=&\dfrac{585}{45}&& \\ \\ &&&&&&d&=&13&& \\ \\ &&&&&&n&=&2(13)&& \\ &&&&&&n&=&26&& \\ \\ &&&&&&q&=&13&-&3 \\ &&&&&&q&=&10&& \end{array}
  24. \begin{array}{rr} \\ \\ \\ \begin{array}{rrrrrcrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &5n&+&10d&+&25q&=&375 \\ &n&+&d&+&q&=&40 \\ &&&&&d&=&3q \\ \\ &(n&+&d&+&q&=&40)(-5) \\ &-5n&-&5d&-&5q&=&-200 \\ +&5n&+&10d&+&25q&=&375 \\ \midrule &&&&&\dfrac{5d+20q}{5}&=&\dfrac{175}{5} \\ \\ &&&d&+&4q&=&35 \\ &&&3q&+&4q&=&35 \\ &&&&&\dfrac{7q}{7}&=&\dfrac{35}{7} \\ \\ &&&&&q&=&5 \\ \\ \end{array} &\hspace{0.25in} \begin{array}{rrrrrrr} \\ \\ \\ \\ &&&&d&=&3(5) \\ &&&&d&=&15 \\ \\ n&+&d&+&q&=&40 \\ n&+&15&+&5&=&40 \\ &&n&+&20&=&40 \\ &&&-&20&&-20 \\ \midrule &&&&n&=&20 \end{array} \end{array}
  25. \begin{array}{rrrrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &&&&S_{22}&=&3&+&4S_{40} \\ &&22S_{22}&+&40S_{40}&=&834&& \\ \\ 22(3&+&4S_{40})&+&40S_{40}&=&834&& \\ 66&+&88S_{40}&+&40S_{40}&=&834&& \\ -66&&&&&&-66&& \\ \midrule &&&&\dfrac{128S_{40}}{128}&=&\dfrac{768}{128}&& \\ \\ &&&&S_{40}&=&6&& \\ \\ &&&&S_{22}&=&3&+&4(6) \\ &&&&S_{22}&=&3&+&24 \\ &&&&S_{22}&=&27&& \end{array}

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Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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