{"id":1523,"date":"2019-06-28T13:30:46","date_gmt":"2019-06-28T17:30:46","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1523"},"modified":"2019-06-28T17:22:00","modified_gmt":"2019-06-28T21:22:00","slug":"answer-key-5-5","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-5-5\/","title":{"raw":"Answer Key 5.5","rendered":"Answer Key 5.5"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\left\\{\r\n\\begin{array}{rrrrr}\r\nd&+&q&=&103 \\\\\r\n10d&+&25q&=&1525\r\n\\end{array}\r\n\\right.\\)<\/li>\r\n \t
  2. \\(\\left\\{\r\n\\begin{array}{rrrrr}\r\nn&+&f&=&34 \\\\\r\n5n&+&50f&=&1340\r\n\\end{array}\r\n\\right.\\)<\/li>\r\n \t
  3. \\(\\left\\{\r\n\\begin{array}{rrrrr}\r\nA&+&C&=&578 \\\\\r\n2A&+&1.5C&=&985\r\n\\end{array}\r\n\\right.\\)<\/li>\r\n \t
  4. \\(\\left\\{\r\n\\begin{array}{rrrrr}\r\nd&+&q&=&21 \\\\\r\n10d&+&25q&=&390\r\n\\end{array}\r\n\\right.\\)<\/li>\r\n \t
  5. \\(\\left\\{\r\n\\begin{array}{rrrrr}\r\n5n&+&10d&=&225 \\\\\r\n&&d&=&2n\r\n\\end{array}\r\n\\right. \\)<\/li>\r\n \t
  6. \\(\\left\\{\r\n\\begin{array}{rrrrrrr}\r\n25q&+&50f&=&375&& \\\\\r\n&&q&=&f&+&3\r\n\\end{array}\r\n\\right. \\)<\/li>\r\n \t
  7. \\(\\left\\{\r\n\\begin{array}{rrrrr}\r\nI_{9.5}&+&I_{11}&=&10000\\phantom{.00} \\\\\r\n0.095I_{9.5}&+&0.11I_{11}&=&1038.50\r\n\\end{array}\r\n\\right. \\)<\/li>\r\n \t
  8. \\(7000(r)+9000(r+0.02)=900\\)<\/li>\r\n \t
  9. \\(1600(r)+2400(2r)=256\\)<\/li>\r\n \t
  10. \\(3000(r)+4500(r-0.02)=435\\)<\/li>\r\n \t
  11. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&N&+&C&=&203 \\\\\r\n&2N&+&1.25C&=&310 \\\\ \\\\\r\n&(N&+&C&=&\\phantom{-}203)(-2) \\\\\r\n&-2N&-&2.00C&=&-406 \\\\\r\n+&2N&+&1.25C&=&\\phantom{-}310 \\\\\r\n\\midrule\r\n&&&\\dfrac{-0.75C}{-0.75}&=&\\dfrac{-96}{-0.75} \\\\ \\\\\r\n&&&C&=&128 \\\\ \\\\\r\n&&&N&=&203-C \\\\\r\n&&&N&=&203-128 \\\\\r\n&&&N&=&75\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&d&+&b&=&131 \\\\\r\n&2.50d&+&2.75b&=&342 \\\\ \\\\\r\n&(d&+&b&=&131)(-2.5) \\\\\r\n&-2.50d&-&2.50b&=&-327.5 \\\\\r\n+&2.50d&+&2.75b&=&\\phantom{-}342 \\\\\r\n\\midrule\r\n&&&\\dfrac{0.25b}{0.25}&=&\\dfrac{14.5}{0.25} \\\\ \\\\\r\n&&&b&=&58 \\\\ \\\\\r\n&&&d&=&131-b \\\\\r\n&&&d&=&131-58 \\\\\r\n&&&d&=&73\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&d&+&q&=&\\phantom{0}27 \\\\\r\n&10d&+&25q&=&495 \\\\ \\\\\r\n&(d&+&q&=&\\phantom{-0}27)(-10) \\\\\r\n&-10d&-&10q&=&-270 \\\\\r\n+&10d&+&25q&=&\\phantom{-}495 \\\\\r\n\\midrule\r\n&&&\\dfrac{15q}{15}&=&\\dfrac{225}{15} \\\\ \\\\\r\n&&&q&=&15 \\\\ \\\\\r\n&&&d&=&27-q \\\\\r\n&&&d&=&27-15 \\\\\r\n&&&d&=&12\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&d&+&n&=&18 \\\\\r\n&10d&+&5n&=&115 \\\\ \\\\\r\n&(d&+&n&=&18)(-5) \\\\\r\n&-5d&-&5n&=&-90 \\\\\r\n+&10d&+&5n&=&115 \\\\\r\n\\midrule\r\n&&&\\dfrac{5d}{5}&=&\\dfrac{25}{5} \\\\ \\\\\r\n&&&d&=&5 \\\\ \\\\\r\n&&&n&=&18-d \\\\\r\n&&&n&=&18-5 \\\\\r\n&&&n&=&13\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&S_{25}&+&S_{20}&=&\\phantom{0}40 \\\\\r\n&25S_{25}&+&20S_{20}&=&960 \\\\ \\\\\r\n&(S_{25}&+&S_{20}&=&40)(-20) \\\\\r\n&-20S_{25}&-&20S_{20}&=&-800 \\\\\r\n+&25S_{25}&+&20S_{20}&=&\\phantom{-}960 \\\\\r\n\\midrule\r\n&&&\\dfrac{5S_{25}}{5}&=&\\dfrac{160}{5} \\\\ \\\\\r\n&&&S_{25}&=&32 \\\\ \\\\\r\n&&&S_{20}&=&40-S_{25} \\\\\r\n&&&S_{20}&=&40-32 \\\\\r\n&&&S_{20}&=&8\r\n\\end{array}\\)<\/li>\r\n \t
  16. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&S_{15}&+&S_{25}&=&\\phantom{0}15 \\\\\r\n&15S_{15}&+&25S_{25}&=&315 \\\\ \\\\\r\n&(S_{15}&+&S_{25}&=&15)(-15) \\\\\r\n&-15S_{15}&-&15S_{25}&=&-225 \\\\\r\n+&15S_{15}&+&25S_{25}&=&\\phantom{-}315 \\\\\r\n\\midrule\r\n&&&\\dfrac{10S_{25}}{10}&=&\\dfrac{90}{10} \\\\ \\\\\r\n&&&S_{25}&=&9 \\\\ \\\\\r\n&&&S_{15}&=&15-S_{25} \\\\\r\n&&&S_{15}&=&15-9 \\\\\r\n&&&S_{15}&=&6\r\n\\end{array}\\)<\/li>\r\n \t
  17. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&I_{12}&+&I_{13}&=&27000 \\\\\r\n&0.12I_{12}&+&0.13I_{13}&=&\\phantom{0}3385 \\\\ \\\\\r\n&(I_{12}&+&I_{13}&=&27000)(-0.12) \\\\\r\n&-0.12I_{12}&-&0.12I_{13}&=&-3240 \\\\\r\n+&0.12I_{12}&+&0.13I_{13}&=&\\phantom{-}3385 \\\\\r\n\\midrule\r\n&&&\\dfrac{0.01I_{13}}{0.01}&=&\\dfrac{145}{0.01} \\\\ \\\\\r\n&&&I_{13}&=&14500 \\\\ \\\\\r\n&&&I_{12}&=&27000-I_{13} \\\\\r\n&&&I_{12}&=&27000-14500 \\\\\r\n&&&I_{12}&=&12500\r\n\\end{array}\\)<\/li>\r\n \t
  18. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&I_5&+&I_{7.5}&=&50000 \\\\\r\n&0.05I_5&+&0.075I_{7.5}&=&3250 \\\\ \\\\\r\n&(I_5&+&I_{7.5}&=&50000)(-0.05) \\\\\r\n&-0.05I_5&-&0.05I_{7.5}&=&-2500 \\\\\r\n+&0.05I_5&+&0.075I_{7.5}&=&\\phantom{-}3250 \\\\\r\n\\midrule\r\n&&&\\dfrac{0.025I_{7.5}}{0.025}&=&\\dfrac{750}{0.025} \\\\ \\\\\r\n&&&I_{7.5}&=&30000 \\\\ \\\\\r\n&&&I_5&=&50000-I_{7.5} \\\\\r\n&&&I_5&=&50000-30000 \\\\\r\n&&&I_5&=&20000\r\n\\end{array}\\)<\/li>\r\n \t
  19. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&10d&+&25q&=&605&& \\\\\r\n&&&&d&=&q&-&6 \\\\ \\\\\r\n10(q&-&6)&+&25q&=&605&& \\\\\r\n10q&-&60&+&25q&=&605&& \\\\\r\n&+&60&&&&+60&& \\\\\r\n\\midrule\r\n&&&&\\dfrac{35q}{35}&=&\\dfrac{665}{35}&& \\\\ \\\\\r\n&&&&q&=&19&& \\\\ \\\\\r\n&&&&d&=&q&-&6 \\\\\r\n&&&&d&=&19&-&6 \\\\\r\n&&&&d&=&13&& \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  20. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&5n&+&10d&=&275&& \\\\\r\n&&&&d&=&2n&-&10 \\\\ \\\\\r\n5n&+&10(2n&-&10)&=&275&& \\\\\r\n5n&+&20n&-&100&=&275&& \\\\\r\n&&&+&100&&+100&& \\\\\r\n\\midrule\r\n&&&&\\dfrac{25n}{25}&=&\\dfrac{375}{25}&& \\\\ \\\\\r\n&&&&n&=&15&& \\\\ \\\\\r\n&&&&d&=&2n&-&10 \\\\\r\n&&&&d&=&2(15)&-&10 \\\\\r\n&&&&d&=&30&-&10 \\\\\r\n&&&&d&=&20&&\r\n\\end{array}\\)<\/li>\r\n \t
  21. \\(\\begin{array}{rrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n3000r&+&24000(r&-&0.04)&=&2010 \\\\\r\n3000r&+&24000r&-&960&=&2010 \\\\\r\n&&&+&960&&+960 \\\\\r\n\\midrule\r\n&&&&\\dfrac{27000r}{27000}&=&\\dfrac{2970}{27000} \\\\ \\\\\r\n&&&&r&=&0.11=11\\% \\\\\r\n&&0.11&-&0.04&=&0.07=7\\% \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  22. \\(\\begin{array}{rrrrcrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n5000r&+&11000\\left(\\dfrac{2}{3}r\\right)&=&1480&& \\\\ \\\\\r\n5000r&+&7333.33r&=&1480&& \\\\ \\\\\r\n&&\\dfrac{12333.33r}{12333.33}&=&\\dfrac{1480}{12333.33}&& \\\\ \\\\\r\n&&r&=&0.12&=&12\\% \\\\ \\\\\r\n&&\\dfrac{2}{3}r&=&0.08&=&8\\%\r\n\\end{array}\\)<\/li>\r\n \t
  23. \\(\\begin{array}{rrrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&5n&+&10d&+&25q&=&510&& \\\\\r\n&&&&&&n&=&2d&& \\\\\r\n&&&&&&q&=&d&-&3 \\\\ \\\\\r\n5(2d)&+&10d&+&25(d&-&3)&=&510&& \\\\\r\n10d&+&10d&+&25d&-&75&=&510&& \\\\\r\n&&&&&+&75&&+75&& \\\\\r\n\\midrule\r\n&&&&&&\\dfrac{45d}{45}&=&\\dfrac{585}{45}&& \\\\ \\\\\r\n&&&&&&d&=&13&& \\\\ \\\\\r\n&&&&&&n&=&2(13)&& \\\\\r\n&&&&&&n&=&26&& \\\\ \\\\\r\n&&&&&&q&=&13&-&3 \\\\\r\n&&&&&&q&=&10&&\r\n\\end{array}\\)<\/li>\r\n \t
  24. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrcrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&5n&+&10d&+&25q&=&375 \\\\\r\n&n&+&d&+&q&=&40 \\\\\r\n&&&&&d&=&3q \\\\ \\\\\r\n&(n&+&d&+&q&=&40)(-5) \\\\\r\n&-5n&-&5d&-&5q&=&-200 \\\\\r\n+&5n&+&10d&+&25q&=&375 \\\\\r\n\\midrule\r\n&&&&&\\dfrac{5d+20q}{5}&=&\\dfrac{175}{5} \\\\ \\\\\r\n&&&d&+&4q&=&35 \\\\\r\n&&&3q&+&4q&=&35 \\\\\r\n&&&&&\\dfrac{7q}{7}&=&\\dfrac{35}{7} \\\\ \\\\\r\n&&&&&q&=&5 \\\\ \\\\\r\n\\end{array}\r\n&\\hspace{0.25in}\r\n\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\\r\n&&&&d&=&3(5) \\\\\r\n&&&&d&=&15 \\\\ \\\\\r\nn&+&d&+&q&=&40 \\\\\r\nn&+&15&+&5&=&40 \\\\\r\n&&n&+&20&=&40 \\\\\r\n&&&-&20&&-20 \\\\\r\n\\midrule\r\n&&&&n&=&20\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  25. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&S_{22}&=&3&+&4S_{40} \\\\\r\n&&22S_{22}&+&40S_{40}&=&834&& \\\\ \\\\\r\n22(3&+&4S_{40})&+&40S_{40}&=&834&& \\\\\r\n66&+&88S_{40}&+&40S_{40}&=&834&& \\\\\r\n-66&&&&&&-66&& \\\\\r\n\\midrule\r\n&&&&\\dfrac{128S_{40}}{128}&=&\\dfrac{768}{128}&& \\\\ \\\\\r\n&&&&S_{40}&=&6&& \\\\ \\\\\r\n&&&&S_{22}&=&3&+&4(6) \\\\\r\n&&&&S_{22}&=&3&+&24 \\\\\r\n&&&&S_{22}&=&27&&\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
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    1. \"\left\{<\/li>\n
    2. \"\left\{<\/li>\n
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    4. \"\left\{<\/li>\n
    5. \"\left\{<\/li>\n
    6. \"\left\{<\/li>\n
    7. \"\left\{<\/li>\n
    8. \"7000(r)+9000(r+0.02)=900\"<\/li>\n
    9. \"1600(r)+2400(2r)=256\"<\/li>\n
    10. \"3000(r)+4500(r-0.02)=435\"<\/li>\n
    11. \"\begin{array}{rrrrrl}<\/li>\n
    12. \"\begin{array}{rrrrrl}<\/li>\n
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    25. \"\begin{array}{rrrrrrrrr}<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":41,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1523","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1523","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/727"}],"version-history":[{"count":4,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1523\/revisions"}],"predecessor-version":[{"id":1527,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1523\/revisions\/1527"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1523\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1523"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1523"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1523"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1523"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}