{"id":1857,"date":"2021-12-02T19:39:44","date_gmt":"2021-12-03T00:39:44","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-5-5\/"},"modified":"2022-11-02T10:37:57","modified_gmt":"2022-11-02T14:37:57","slug":"answer-key-5-5","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-5-5\/","title":{"raw":"Answer Key 5.5","rendered":"Answer Key 5.5"},"content":{"raw":"
    \n \t
  1. [latex]\\left\\{\n\\begin{array}{rrrrr}\nd&+&q&=&103 \\\\\n10d&+&25q&=&1525\n\\end{array}\n\\right.[\/latex]<\/li>\n \t
  2. [latex]\\left\\{\n\\begin{array}{rrrrr}\nn&+&f&=&34 \\\\\n5n&+&50f&=&1340\n\\end{array}\n\\right.[\/latex]<\/li>\n \t
  3. [latex]\\left\\{\n\\begin{array}{rrrrr}\nA&+&C&=&578 \\\\\n2A&+&1.5C&=&985\n\\end{array}\n\\right.[\/latex]<\/li>\n \t
  4. [latex]\\left\\{\n\\begin{array}{rrrrr}\nd&+&q&=&21 \\\\\n10d&+&25q&=&390\n\\end{array}\n\\right.[\/latex]<\/li>\n \t
  5. [latex]\\left\\{\n\\begin{array}{rrrrr}\n5n&+&10d&=&225 \\\\\n&&d&=&2n\n\\end{array}\n\\right. [\/latex]<\/li>\n \t
  6. [latex]\\left\\{\n\\begin{array}{rrrrrrr}\n25q&+&50f&=&375&& \\\\\n&&q&=&f&+&3\n\\end{array}\n\\right. [\/latex]<\/li>\n \t
  7. [latex]\\left\\{\n\\begin{array}{rrrrr}\nI_{9.5}&+&I_{11}&=&10000\\phantom{.00} \\\\\n0.095I_{9.5}&+&0.11I_{11}&=&1038.50\n\\end{array}\n\\right. [\/latex]<\/li>\n \t
  8. [latex]7000(r)+9000(r+0.02)=900[\/latex]<\/li>\n \t
  9. [latex]1600(r)+2400(2r)=256[\/latex]<\/li>\n \t
  10. [latex]3000(r)+4500(r-0.02)=435[\/latex]<\/li>\n \t
  11. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&N&+&C&=&203 \\\\\n&2N&+&1.25C&=&310 \\\\ \\\\\n&(N&+&C&=&\\phantom{-}203)(-2) \\\\\n&-2N&-&2.00C&=&-406 \\\\\n+&2N&+&1.25C&=&\\phantom{-}310 \\\\\n\\hline\n&&&\\dfrac{-0.75C}{-0.75}&=&\\dfrac{-96}{-0.75} \\\\ \\\\\n&&&C&=&128 \\\\ \\\\\n&&&N&=&203-C \\\\\n&&&N&=&203-128 \\\\\n&&&N&=&75\n\\end{array}[\/latex]<\/li>\n \t
  12. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&d&+&b&=&131 \\\\\n&2.50d&+&2.75b&=&342 \\\\ \\\\\n&(d&+&b&=&131)(-2.5) \\\\\n&-2.50d&-&2.50b&=&-327.5 \\\\\n+&2.50d&+&2.75b&=&\\phantom{-}342 \\\\\n\\hline\n&&&\\dfrac{0.25b}{0.25}&=&\\dfrac{14.5}{0.25} \\\\ \\\\\n&&&b&=&58 \\\\ \\\\\n&&&d&=&131-b \\\\\n&&&d&=&131-58 \\\\\n&&&d&=&73\n\\end{array}[\/latex]<\/li>\n \t
  13. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&d&+&q&=&\\phantom{0}27 \\\\\n&10d&+&25q&=&495 \\\\ \\\\\n&(d&+&q&=&\\phantom{-0}27)(-10) \\\\\n&-10d&-&10q&=&-270 \\\\\n+&10d&+&25q&=&\\phantom{-}495 \\\\\n\\hline\n&&&\\dfrac{15q}{15}&=&\\dfrac{225}{15} \\\\ \\\\\n&&&q&=&15 \\\\ \\\\\n&&&d&=&27-q \\\\\n&&&d&=&27-15 \\\\\n&&&d&=&12\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&d&+&n&=&18 \\\\\n&10d&+&5n&=&115 \\\\ \\\\\n&(d&+&n&=&18)(-5) \\\\\n&-5d&-&5n&=&-90 \\\\\n+&10d&+&5n&=&115 \\\\\n\\hline\n&&&\\dfrac{5d}{5}&=&\\dfrac{25}{5} \\\\ \\\\\n&&&d&=&5 \\\\ \\\\\n&&&n&=&18-d \\\\\n&&&n&=&18-5 \\\\\n&&&n&=&13\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&S_{25}&+&S_{20}&=&\\phantom{0}40 \\\\\n&25S_{25}&+&20S_{20}&=&960 \\\\ \\\\\n&(S_{25}&+&S_{20}&=&40)(-20) \\\\\n&-20S_{25}&-&20S_{20}&=&-800 \\\\\n+&25S_{25}&+&20S_{20}&=&\\phantom{-}960 \\\\\n\\hline\n&&&\\dfrac{5S_{25}}{5}&=&\\dfrac{160}{5} \\\\ \\\\\n&&&S_{25}&=&32 \\\\ \\\\\n&&&S_{20}&=&40-S_{25} \\\\\n&&&S_{20}&=&40-32 \\\\\n&&&S_{20}&=&8\n\\end{array}[\/latex]<\/li>\n \t
  16. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&S_{15}&+&S_{25}&=&\\phantom{0}15 \\\\\n&15S_{15}&+&25S_{25}&=&315 \\\\ \\\\\n&(S_{15}&+&S_{25}&=&15)(-15) \\\\\n&-15S_{15}&-&15S_{25}&=&-225 \\\\\n+&15S_{15}&+&25S_{25}&=&\\phantom{-}315 \\\\\n\\hline\n&&&\\dfrac{10S_{25}}{10}&=&\\dfrac{90}{10} \\\\ \\\\\n&&&S_{25}&=&9 \\\\ \\\\\n&&&S_{15}&=&15-S_{25} \\\\\n&&&S_{15}&=&15-9 \\\\\n&&&S_{15}&=&6\n\\end{array}[\/latex]<\/li>\n \t
  17. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&I_{12}&+&I_{13}&=&27000 \\\\\n&0.12I_{12}&+&0.13I_{13}&=&\\phantom{0}3385 \\\\ \\\\\n&(I_{12}&+&I_{13}&=&27000)(-0.12) \\\\\n&-0.12I_{12}&-&0.12I_{13}&=&-3240 \\\\\n+&0.12I_{12}&+&0.13I_{13}&=&\\phantom{-}3385 \\\\\n\\hline\n&&&\\dfrac{0.01I_{13}}{0.01}&=&\\dfrac{145}{0.01} \\\\ \\\\\n&&&I_{13}&=&14500 \\\\ \\\\\n&&&I_{12}&=&27000-I_{13} \\\\\n&&&I_{12}&=&27000-14500 \\\\\n&&&I_{12}&=&12500\n\\end{array}[\/latex]<\/li>\n \t
  18. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&I_5&+&I_{7.5}&=&50000 \\\\\n&0.05I_5&+&0.075I_{7.5}&=&3250 \\\\ \\\\\n&(I_5&+&I_{7.5}&=&50000)(-0.05) \\\\\n&-0.05I_5&-&0.05I_{7.5}&=&-2500 \\\\\n+&0.05I_5&+&0.075I_{7.5}&=&\\phantom{-}3250 \\\\\n\\hline\n&&&\\dfrac{0.025I_{7.5}}{0.025}&=&\\dfrac{750}{0.025} \\\\ \\\\\n&&&I_{7.5}&=&30000 \\\\ \\\\\n&&&I_5&=&50000-I_{7.5} \\\\\n&&&I_5&=&50000-30000 \\\\\n&&&I_5&=&20000\n\\end{array}[\/latex]<\/li>\n \t
  19. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n&&10d&+&25q&=&605&& \\\\\n&&&&d&=&q&-&6 \\\\ \\\\\n10(q&-&6)&+&25q&=&605&& \\\\\n10q&-&60&+&25q&=&605&& \\\\\n&+&60&&&&+60&& \\\\\n\\hline\n&&&&\\dfrac{35q}{35}&=&\\dfrac{665}{35}&& \\\\ \\\\\n&&&&q&=&19&& \\\\ \\\\\n&&&&d&=&q&-&6 \\\\\n&&&&d&=&19&-&6 \\\\\n&&&&d&=&13&& \\\\\n\\end{array}[\/latex]<\/li>\n \t
  20. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n&&5n&+&10d&=&275&& \\\\\n&&&&d&=&2n&-&10 \\\\ \\\\\n5n&+&10(2n&-&10)&=&275&& \\\\\n5n&+&20n&-&100&=&275&& \\\\\n&&&+&100&&+100&& \\\\\n\\hline\n&&&&\\dfrac{25n}{25}&=&\\dfrac{375}{25}&& \\\\ \\\\\n&&&&n&=&15&& \\\\ \\\\\n&&&&d&=&2n&-&10 \\\\\n&&&&d&=&2(15)&-&10 \\\\\n&&&&d&=&30&-&10 \\\\\n&&&&d&=&20&&\n\\end{array}[\/latex]<\/li>\n \t
  21. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrl}\n3000r&+&24000(r&-&0.04)&=&2010 \\\\\n3000r&+&24000r&-&960&=&2010 \\\\\n&&&+&960&&+960 \\\\\n\\hline\n&&&&\\dfrac{27000r}{27000}&=&\\dfrac{2970}{27000} \\\\ \\\\\n&&&&r&=&0.11=11\\% \\\\\n&&0.11&-&0.04&=&0.07=7\\% \\\\\n\\end{array}[\/latex]<\/li>\n \t
  22. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrcrr}\n5000r&+&11000\\left(\\dfrac{2}{3}r\\right)&=&1480&& \\\\ \\\\\n5000r&+&7333.33r&=&1480&& \\\\ \\\\\n&&\\dfrac{12333.33r}{12333.33}&=&\\dfrac{1480}{12333.33}&& \\\\ \\\\\n&&r&=&0.12&=&12\\% \\\\ \\\\\n&&\\dfrac{2}{3}r&=&0.08&=&8\\%\n\\end{array}[\/latex]<\/li>\n \t
  23. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrrr}\n&&5n&+&10d&+&25q&=&510&& \\\\\n&&&&&&n&=&2d&& \\\\\n&&&&&&q&=&d&-&3 \\\\ \\\\\n5(2d)&+&10d&+&25(d&-&3)&=&510&& \\\\\n10d&+&10d&+&25d&-&75&=&510&& \\\\\n&&&&&+&75&&+75&& \\\\\n\\hline\n&&&&&&\\dfrac{45d}{45}&=&\\dfrac{585}{45}&& \\\\ \\\\\n&&&&&&d&=&13&& \\\\ \\\\\n&&&&&&n&=&2(13)&& \\\\\n&&&&&&n&=&26&& \\\\ \\\\\n&&&&&&q&=&13&-&3 \\\\\n&&&&&&q&=&10&&\n\\end{array}[\/latex]<\/li>\n \t
  24. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rr}\n\\begin{array}[t]{rrrrrcrr}\n&5n&+&10d&+&25q&=&375 \\\\\n&n&+&d&+&q&=&40 \\\\\n&&&&&d&=&3q \\\\ \\\\\n&(n&+&d&+&q&=&40)(-5) \\\\\n&-5n&-&5d&-&5q&=&-200 \\\\\n+&5n&+&10d&+&25q&=&375 \\\\\n\\hline\n&&&&&\\dfrac{5d+20q}{5}&=&\\dfrac{175}{5} \\\\ \\\\\n&&&d&+&4q&=&35 \\\\\n&&&3q&+&4q&=&35 \\\\\n&&&&&\\dfrac{7q}{7}&=&\\dfrac{35}{7} \\\\ \\\\\n&&&&&q&=&5 \\\\ \\\\\n\\end{array}\n&\\hspace{0.25in}\n\\begin{array}[t]{rrrrrrr}\n&&&&d&=&3(5) \\\\\n&&&&d&=&15 \\\\ \\\\\nn&+&d&+&q&=&40 \\\\\nn&+&15&+&5&=&40 \\\\\n&&n&+&20&=&40 \\\\\n&&&-&20&&-20 \\\\\n\\hline\n&&&&n&=&20\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  25. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n&&&&S_{22}&=&3&+&4S_{40} \\\\\n&&22S_{22}&+&40S_{40}&=&834&& \\\\ \\\\\n22(3&+&4S_{40})&+&40S_{40}&=&834&& \\\\\n66&+&88S_{40}&+&40S_{40}&=&834&& \\\\\n-66&&&&&&-66&& \\\\\n\\hline\n&&&&\\dfrac{128S_{40}}{128}&=&\\dfrac{768}{128}&& \\\\ \\\\\n&&&&S_{40}&=&6&& \\\\ \\\\\n&&&&S_{22}&=&3&+&4(6) \\\\\n&&&&S_{22}&=&3&+&24 \\\\\n&&&&S_{22}&=&27&&\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]\\left\\{ \\begin{array}{rrrrr} d&+&q&=&103 \\\\ 10d&+&25q&=&1525 \\end{array} \\right.[\/latex]<\/li>\n
    2. [latex]\\left\\{ \\begin{array}{rrrrr} n&+&f&=&34 \\\\ 5n&+&50f&=&1340 \\end{array} \\right.[\/latex]<\/li>\n
    3. [latex]\\left\\{ \\begin{array}{rrrrr} A&+&C&=&578 \\\\ 2A&+&1.5C&=&985 \\end{array} \\right.[\/latex]<\/li>\n
    4. [latex]\\left\\{ \\begin{array}{rrrrr} d&+&q&=&21 \\\\ 10d&+&25q&=&390 \\end{array} \\right.[\/latex]<\/li>\n
    5. [latex]\\left\\{ \\begin{array}{rrrrr} 5n&+&10d&=&225 \\\\ &&d&=&2n \\end{array} \\right.[\/latex]<\/li>\n
    6. [latex]\\left\\{ \\begin{array}{rrrrrrr} 25q&+&50f&=&375&& \\\\ &&q&=&f&+&3 \\end{array} \\right.[\/latex]<\/li>\n
    7. [latex]\\left\\{ \\begin{array}{rrrrr} I_{9.5}&+&I_{11}&=&10000\\phantom{.00} \\\\ 0.095I_{9.5}&+&0.11I_{11}&=&1038.50 \\end{array} \\right.[\/latex]<\/li>\n
    8. [latex]7000(r)+9000(r+0.02)=900[\/latex]<\/li>\n
    9. [latex]1600(r)+2400(2r)=256[\/latex]<\/li>\n
    10. [latex]3000(r)+4500(r-0.02)=435[\/latex]<\/li>\n
    11. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{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}[\/latex]<\/li>\n
    12. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{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}[\/latex]<\/li>\n
    13. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{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}[\/latex]<\/li>\n
    14. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{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}[\/latex]<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{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}[\/latex]<\/li>\n
    16. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{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}[\/latex]<\/li>\n
    17. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{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}[\/latex]<\/li>\n
    18. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{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}[\/latex]<\/li>\n
    19. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{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}[\/latex]<\/li>\n
    20. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{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}[\/latex]<\/li>\n
    21. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{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}[\/latex]<\/li>\n
    22. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{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}[\/latex]<\/li>\n
    23. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{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}[\/latex]<\/li>\n
    24. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rr} \\begin{array}[t]{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}[t]{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}[\/latex]<\/li>\n
    25. [latex]\\phantom{a}[\/latex]
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