Answer Key 5.5
- \(\left\{
\begin{array}{rrrrr}
d&+&q&=&103 \\
10d&+&25q&=&1525
\end{array}
\right.\) - \(\left\{
\begin{array}{rrrrr}
n&+&f&=&34 \\
5n&+&50f&=&1340
\end{array}
\right.\) - \(\left\{
\begin{array}{rrrrr}
A&+&C&=&578 \\
2A&+&1.5C&=&985
\end{array}
\right.\) - \(\left\{
\begin{array}{rrrrr}
d&+&q&=&21 \\
10d&+&25q&=&390
\end{array}
\right.\) - \(\left\{
\begin{array}{rrrrr}
5n&+&10d&=&225 \\
&&d&=&2n
\end{array}
\right. \) - \(\left\{
\begin{array}{rrrrrrr}
25q&+&50f&=&375&& \\
&&q&=&f&+&3
\end{array}
\right. \) - \(\left\{
\begin{array}{rrrrr}
I_{9.5}&+&I_{11}&=&10000\phantom{.00} \\
0.095I_{9.5}&+&0.11I_{11}&=&1038.50
\end{array}
\right. \) - \(7000(r)+9000(r+0.02)=900\)
- \(1600(r)+2400(2r)=256\)
- \(3000(r)+4500(r-0.02)=435\)
- \(\begin{array}{rrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
&N&+&C&=&203 \\
&2N&+&1.25C&=&310 \\ \\
&(N&+&C&=&\phantom{-}203)(-2) \\
&-2N&-&2.00C&=&-406 \\
+&2N&+&1.25C&=&\phantom{-}310 \\
\hline
&&&\dfrac{-0.75C}{-0.75}&=&\dfrac{-96}{-0.75} \\ \\
&&&C&=&128 \\ \\
&&&N&=&203-C \\
&&&N&=&203-128 \\
&&&N&=&75
\end{array}\) - \(\begin{array}{rrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
&d&+&b&=&131 \\
&2.50d&+&2.75b&=&342 \\ \\
&(d&+&b&=&131)(-2.5) \\
&-2.50d&-&2.50b&=&-327.5 \\
+&2.50d&+&2.75b&=&\phantom{-}342 \\
\hline
&&&\dfrac{0.25b}{0.25}&=&\dfrac{14.5}{0.25} \\ \\
&&&b&=&58 \\ \\
&&&d&=&131-b \\
&&&d&=&131-58 \\
&&&d&=&73
\end{array}\) - \(\begin{array}{rrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
&d&+&q&=&\phantom{0}27 \\
&10d&+&25q&=&495 \\ \\
&(d&+&q&=&\phantom{-0}27)(-10) \\
&-10d&-&10q&=&-270 \\
+&10d&+&25q&=&\phantom{-}495 \\
\hline
&&&\dfrac{15q}{15}&=&\dfrac{225}{15} \\ \\
&&&q&=&15 \\ \\
&&&d&=&27-q \\
&&&d&=&27-15 \\
&&&d&=&12
\end{array}\) - \(\begin{array}{rrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
&d&+&n&=&18 \\
&10d&+&5n&=&115 \\ \\
&(d&+&n&=&18)(-5) \\
&-5d&-&5n&=&-90 \\
+&10d&+&5n&=&115 \\
\hline
&&&\dfrac{5d}{5}&=&\dfrac{25}{5} \\ \\
&&&d&=&5 \\ \\
&&&n&=&18-d \\
&&&n&=&18-5 \\
&&&n&=&13
\end{array}\) - \(\begin{array}{rrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
&S_{25}&+&S_{20}&=&\phantom{0}40 \\
&25S_{25}&+&20S_{20}&=&960 \\ \\
&(S_{25}&+&S_{20}&=&40)(-20) \\
&-20S_{25}&-&20S_{20}&=&-800 \\
+&25S_{25}&+&20S_{20}&=&\phantom{-}960 \\
\hline
&&&\dfrac{5S_{25}}{5}&=&\dfrac{160}{5} \\ \\
&&&S_{25}&=&32 \\ \\
&&&S_{20}&=&40-S_{25} \\
&&&S_{20}&=&40-32 \\
&&&S_{20}&=&8
\end{array}\) - \(\begin{array}{rrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
&S_{15}&+&S_{25}&=&\phantom{0}15 \\
&15S_{15}&+&25S_{25}&=&315 \\ \\
&(S_{15}&+&S_{25}&=&15)(-15) \\
&-15S_{15}&-&15S_{25}&=&-225 \\
+&15S_{15}&+&25S_{25}&=&\phantom{-}315 \\
\hline
&&&\dfrac{10S_{25}}{10}&=&\dfrac{90}{10} \\ \\
&&&S_{25}&=&9 \\ \\
&&&S_{15}&=&15-S_{25} \\
&&&S_{15}&=&15-9 \\
&&&S_{15}&=&6
\end{array}\) - \(\begin{array}{rrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
&I_{12}&+&I_{13}&=&27000 \\
&0.12I_{12}&+&0.13I_{13}&=&\phantom{0}3385 \\ \\
&(I_{12}&+&I_{13}&=&27000)(-0.12) \\
&-0.12I_{12}&-&0.12I_{13}&=&-3240 \\
+&0.12I_{12}&+&0.13I_{13}&=&\phantom{-}3385 \\
\hline
&&&\dfrac{0.01I_{13}}{0.01}&=&\dfrac{145}{0.01} \\ \\
&&&I_{13}&=&14500 \\ \\
&&&I_{12}&=&27000-I_{13} \\
&&&I_{12}&=&27000-14500 \\
&&&I_{12}&=&12500
\end{array}\) - \(\begin{array}{rrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
&I_5&+&I_{7.5}&=&50000 \\
&0.05I_5&+&0.075I_{7.5}&=&3250 \\ \\
&(I_5&+&I_{7.5}&=&50000)(-0.05) \\
&-0.05I_5&-&0.05I_{7.5}&=&-2500 \\
+&0.05I_5&+&0.075I_{7.5}&=&\phantom{-}3250 \\
\hline
&&&\dfrac{0.025I_{7.5}}{0.025}&=&\dfrac{750}{0.025} \\ \\
&&&I_{7.5}&=&30000 \\ \\
&&&I_5&=&50000-I_{7.5} \\
&&&I_5&=&50000-30000 \\
&&&I_5&=&20000
\end{array}\) - \(\begin{array}{rrrrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
&&10d&+&25q&=&605&& \\
&&&&d&=&q&-&6 \\ \\
10(q&-&6)&+&25q&=&605&& \\
10q&-&60&+&25q&=&605&& \\
&+&60&&&&+60&& \\
\hline
&&&&\dfrac{35q}{35}&=&\dfrac{665}{35}&& \\ \\
&&&&q&=&19&& \\ \\
&&&&d&=&q&-&6 \\
&&&&d&=&19&-&6 \\
&&&&d&=&13&& \\
\end{array}\) - \(\begin{array}{rrrrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
&&5n&+&10d&=&275&& \\
&&&&d&=&2n&-&10 \\ \\
5n&+&10(2n&-&10)&=&275&& \\
5n&+&20n&-&100&=&275&& \\
&&&+&100&&+100&& \\
\hline
&&&&\dfrac{25n}{25}&=&\dfrac{375}{25}&& \\ \\
&&&&n&=&15&& \\ \\
&&&&d&=&2n&-&10 \\
&&&&d&=&2(15)&-&10 \\
&&&&d&=&30&-&10 \\
&&&&d&=&20&&
\end{array}\) - \(\begin{array}{rrrrrrl}
\\ \\ \\ \\ \\ \\ \\
3000r&+&24000(r&-&0.04)&=&2010 \\
3000r&+&24000r&-&960&=&2010 \\
&&&+&960&&+960 \\
\hline
&&&&\dfrac{27000r}{27000}&=&\dfrac{2970}{27000} \\ \\
&&&&r&=&0.11=11\% \\
&&0.11&-&0.04&=&0.07=7\% \\
\end{array}\) - \(\begin{array}{rrrrcrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\
5000r&+&11000\left(\dfrac{2}{3}r\right)&=&1480&& \\ \\
5000r&+&7333.33r&=&1480&& \\ \\
&&\dfrac{12333.33r}{12333.33}&=&\dfrac{1480}{12333.33}&& \\ \\
&&r&=&0.12&=&12\% \\ \\
&&\dfrac{2}{3}r&=&0.08&=&8\%
\end{array}\) - \(\begin{array}{rrrrrrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
&&5n&+&10d&+&25q&=&510&& \\
&&&&&&n&=&2d&& \\
&&&&&&q&=&d&-&3 \\ \\
5(2d)&+&10d&+&25(d&-&3)&=&510&& \\
10d&+&10d&+&25d&-&75&=&510&& \\
&&&&&+&75&&+75&& \\
\hline
&&&&&&\dfrac{45d}{45}&=&\dfrac{585}{45}&& \\ \\
&&&&&&d&=&13&& \\ \\
&&&&&&n&=&2(13)&& \\
&&&&&&n&=&26&& \\ \\
&&&&&&q&=&13&-&3 \\
&&&&&&q&=&10&&
\end{array}\) - \(\begin{array}{rr}
\\ \\ \\
\begin{array}{rrrrrcrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
&5n&+&10d&+&25q&=&375 \\
&n&+&d&+&q&=&40 \\
&&&&&d&=&3q \\ \\
&(n&+&d&+&q&=&40)(-5) \\
&-5n&-&5d&-&5q&=&-200 \\
+&5n&+&10d&+&25q&=&375 \\
\hline
&&&&&\dfrac{5d+20q}{5}&=&\dfrac{175}{5} \\ \\
&&&d&+&4q&=&35 \\
&&&3q&+&4q&=&35 \\
&&&&&\dfrac{7q}{7}&=&\dfrac{35}{7} \\ \\
&&&&&q&=&5 \\ \\
\end{array}
&\hspace{0.25in}
\begin{array}{rrrrrrr}
\\ \\ \\ \\
&&&&d&=&3(5) \\
&&&&d&=&15 \\ \\
n&+&d&+&q&=&40 \\
n&+&15&+&5&=&40 \\
&&n&+&20&=&40 \\
&&&-&20&&-20 \\
\hline
&&&&n&=&20
\end{array}
\end{array}\) - \(\begin{array}{rrrrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
&&&&S_{22}&=&3&+&4S_{40} \\
&&22S_{22}&+&40S_{40}&=&834&& \\ \\
22(3&+&4S_{40})&+&40S_{40}&=&834&& \\
66&+&88S_{40}&+&40S_{40}&=&834&& \\
-66&&&&&&-66&& \\
\hline
&&&&\dfrac{128S_{40}}{128}&=&\dfrac{768}{128}&& \\ \\
&&&&S_{40}&=&6&& \\ \\
&&&&S_{22}&=&3&+&4(6) \\
&&&&S_{22}&=&3&+&24 \\
&&&&S_{22}&=&27&&
\end{array}\)
