{"id":1891,"date":"2021-12-02T19:39:51","date_gmt":"2021-12-03T00:39:51","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-6-8\/"},"modified":"2022-11-02T10:38:10","modified_gmt":"2022-11-02T14:38:10","slug":"answer-key-6-8","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-6-8\/","title":{"raw":"Answer Key 6.8","rendered":"Answer Key 6.8"},"content":{"raw":"
    \n \t
  1. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    S40<\/sub><\/th>\n8000<\/td>\n0.40<\/td>\n0.40 (8000)<\/td>\n<\/tr>\n
    W<\/th>\n[latex]x[\/latex]<\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n
    S30<\/sub><\/th>\n[latex]x+8000[\/latex]<\/td>\n0.30<\/td>\n[latex]0.30(x+8000)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]0.40(8000)=0.30(x+8000)[\/latex]<\/li>\n \t
  2. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    A100<\/sub><\/th>\n[latex]x[\/latex]<\/td>\n1.00<\/td>\n[latex]1.00x[\/latex]<\/td>\n<\/tr>\n
    A30<\/sub><\/th>\n5<\/td>\n0.30<\/td>\n0.30 (5)<\/td>\n<\/tr>\n
    A50<\/sub><\/th>\n[latex]x+5[\/latex]<\/td>\n0.50<\/td>\n[latex]0.50(x+5)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]1.00x+0.30(5)=0.50(x+5)[\/latex]<\/li>\n \t
  3. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    S10<\/sub><\/th>\n12<\/td>\n0.10<\/td>\n0.10 (12)<\/td>\n<\/tr>\n
    S3<\/sub><\/th>\n[latex]x[\/latex]<\/td>\n0.03<\/td>\n[latex]0.03 (x)[\/latex]<\/td>\n<\/tr>\n
    S5<\/sub><\/th>\n[latex]x+12[\/latex]<\/td>\n0.05<\/td>\n[latex]0.05(x+12)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]0.10(12)+0.03(x)=0.05(x+12)[\/latex]<\/li>\n \t
  4. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    A100<\/sub><\/th>\n[latex]x[\/latex]<\/td>\n1.00<\/td>\n[latex]1.00x[\/latex]<\/td>\n<\/tr>\n
    A14<\/sub><\/th>\n24<\/td>\n0.14<\/td>\n0.14 (24)<\/td>\n<\/tr>\n
    A20<\/sub><\/th>\n[latex]x+24[\/latex]<\/td>\n0.20<\/td>\n[latex]0.20(x+24)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]1.00x+0.14(24)=0.20(x+24)[\/latex]<\/li>\n \t
  5. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    B<\/th>\n[latex]x[\/latex]<\/td>\n1.60<\/td>\n[latex]1.60x[\/latex]<\/td>\n<\/tr>\n
    Mag<\/th>\n18<\/td>\n2.50<\/td>\n2.50 (18)<\/td>\n<\/tr>\n
    Mix<\/th>\n[latex]x+18[\/latex]<\/td>\n1.90<\/td>\n[latex]1.90(x+18)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]1.60x+2.50(18)=1.90(x+18)[\/latex]<\/li>\n \t
  6. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    A100<\/sub><\/th>\n[latex]x[\/latex]<\/td>\n1.00<\/td>\n[latex]1.00x[\/latex]<\/td>\n<\/tr>\n
    A20<\/sub><\/th>\n40<\/td>\n0.20<\/td>\n0.20 (40)<\/td>\n<\/tr>\n
    A36<\/sub><\/th>\n[latex]x+40[\/latex]<\/td>\n0.36<\/td>\n[latex]0.36(x+40)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]x+0.20(40)=0.36(x+40)[\/latex]<\/li>\n \t
  7. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    O40<\/sub><\/th>\n100<\/td>\n0.40<\/td>\n100 (0.40)<\/td>\n<\/tr>\n
    O100<\/sub><\/th>\n[latex]x[\/latex]<\/td>\n1.00<\/td>\n[latex]x(1.00)[\/latex]<\/td>\n<\/tr>\n
    O50<\/sub><\/th>\n[latex]100+x[\/latex]<\/td>\n0.50<\/td>\n[latex](100+x)(0.50)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]100(0.40)+x=(100+x)(0.50)[\/latex]<\/li>\n \t
  8. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    P220<\/sub><\/th>\n20<\/td>\n220<\/td>\n220 (20)<\/td>\n<\/tr>\n
    P400<\/sub><\/th>\n[latex]x[\/latex]<\/td>\n400<\/td>\n[latex]400(x)[\/latex]<\/td>\n<\/tr>\n
    P300<\/sub><\/th>\n[latex]x+20[\/latex]<\/td>\n300<\/td>\n[latex]300(x+20)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]220(20)+400x=300(x+20)[\/latex]<\/li>\n \t
  9. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    T4.20<\/sub><\/th>\n[latex]x[\/latex]<\/td>\n4.20<\/td>\n[latex]4.20(x)[\/latex]<\/td>\n<\/tr>\n
    T2.25<\/sub><\/th>\n12<\/td>\n2.25<\/td>\n2.25 (12)<\/td>\n<\/tr>\n
    T3.40<\/sub><\/th>\n[latex]x+12[\/latex]<\/td>\n3.40<\/td>\n[latex]3.40(x+12)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]4.20x+2.25(12)=3.40(x+12)[\/latex]<\/li>\n \t
  10. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    S80<\/sub><\/th>\n[latex]x[\/latex]<\/td>\n80<\/td>\n[latex]80(x)[\/latex]<\/td>\n<\/tr>\n
    S25<\/sub><\/th>\n6<\/td>\n25<\/td>\n25 (6)<\/td>\n<\/tr>\n
    S36<\/sub><\/th>\n[latex]x+6[\/latex]<\/td>\n36<\/td>\n[latex]36(x+6)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrrrr}\n80x&+&25(6)&=&36(x&+&6) \\\\\n80x&+&150&=&36x&+&216 \\\\\n-36x&-&150&&-36x&-&150 \\\\\n\\hline\n&&\\dfrac{44x}{44}&=&\\dfrac{66}{44}&& \\\\ \\\\\n&&x&=&\\dfrac{3}{2}&\\text{ or }&1.5 \\text{ L}\n\\end{array}[\/latex]<\/li>\n \t
  11. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    C<\/th>\n[latex]x[\/latex]<\/td>\n7.50<\/td>\n[latex]7.50(x)[\/latex]<\/td>\n<\/tr>\n
    J<\/th>\n24<\/td>\n3.25<\/td>\n3.25 (24)<\/td>\n<\/tr>\n
    M<\/th>\n[latex]x+24[\/latex]<\/td>\n4.50<\/td>\n[latex]4.50(x+24)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrrrr}\n7.50x&+&3.25(24)&=&4.50(x&+&24) \\\\\n7.50x&+&78&=&4.50x&+&108 \\\\\n-4.50x&-&78&&-4.50x&-&78 \\\\\n\\hline\n&&\\dfrac{3.00x}{3.00}&=&\\dfrac{30}{3.00}&& \\\\ \\\\\n&&x&=&10 \\text{ kg}&&\n\\end{array}[\/latex]<\/li>\n \t
  12. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    S<\/th>\n[latex]x[\/latex]<\/td>\n7.00<\/td>\n[latex]7.00(x)[\/latex]<\/td>\n<\/tr>\n
    A<\/th>\n20<\/td>\n3.50<\/td>\n3.50 (20)<\/td>\n<\/tr>\n
    F<\/th>\n[latex]x+20[\/latex]<\/td>\n4.50<\/td>\n[latex]4.50(x+20)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrrrr}\n7.00(x)&+&3.50(20)&=&4.50(x&+&20) \\\\\n7.00x&+&70&=&4.50x&+&90 \\\\\n-4.50x&-&70&&-4.50x&-&70 \\\\\n\\hline\n&&\\dfrac{2.5x}{2.5}&=&\\dfrac{20}{2.5}&& \\\\ \\\\\n&&x&=&8&&\n\\end{array}[\/latex]<\/li>\n \t
  13. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    C1.8<\/sub><\/th>\nC1.8<\/sub><\/td>\n1.80<\/td>\n1.80 (C1.8<\/sub>)<\/td>\n<\/tr>\n
    C3.0<\/sub><\/th>\n15 \u2212 C1.8<\/sub><\/td>\n3.00<\/td>\n3.00 (15 \u2212 C1.8<\/sub>)<\/td>\n<\/tr>\n
    C2.2<\/sub><\/th>\n15<\/td>\n2.20<\/td>\n2.20 (15)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrrrl}\n1.80C_{1.8}&+&3.00(15&-&C_{1.8})&=&2.20(15) \\\\\n1.80C_{1.8}&+&45&-&3C_{1.8}&=&\\phantom{-}33 \\\\\n&-&45&&&&-45 \\\\\n\\hline\n&&&&\\dfrac{-1.2C_{1.8}}{-1.2}&=&\\dfrac{-12}{-1.2} \\\\ \\\\\n&&&&C_{1.8}&=&10 \\\\\n&&&&C_{3.0}&=&15-10 \\\\\n&&&&C_{3.0}&=&5\n\\end{array}[\/latex]<\/li>\n \t
  14. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    M10<\/sub><\/th>\n100 \u2212 C<\/td>\n0.10<\/td>\n0.10 (100 \u2212 C)<\/td>\n<\/tr>\n
    C<\/th>\nC<\/td>\n0.60<\/td>\n0.60 (C)<\/td>\n<\/tr>\n
    M45<\/sub><\/th>\n100<\/td>\n0.45<\/td>\n0.45 (100)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrrrl}\n0.10(100&-&C)&+&0.60(C)&=&0.45(100) \\\\\n10&-&0.10C&+&0.60C&=&\\phantom{-}45 \\\\\n-10&&&&&&-10 \\\\\n\\hline\n&&&&\\dfrac{0.50C}{0.50}&=&\\dfrac{35}{0.50} \\\\ \\\\\n&&&&C&=&70 \\\\\n&&&&M_{10}&=&100-70 \\\\\n&&&&M_{10}&=&30\n\\end{array}[\/latex]<\/li>\n \t
  15. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    A<\/th>\nA<\/td>\n0.50<\/td>\n0.50A<\/td>\n<\/tr>\n
    B<\/th>\n100 cc \u2212 A<\/td>\n0.80<\/td>\n0.80 (100 \u2212 A)<\/td>\n<\/tr>\n
    Mix<\/th>\n100 cc<\/td>\n0.68<\/td>\n0.68 (100)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrrrl}\n0.50A&+&0.80(100&-&A)&=&0.68(100) \\\\\n0.50A&+&80&-&0.80A&=&\\phantom{-}68 \\\\\n&-&80&&&=&-80 \\\\\n\\hline\n&&&&\\dfrac{-0.30A}{-0.30}&=&\\dfrac{-12}{-0.30} \\\\ \\\\\n&&&&A&=&40 \\text{ cc} \\\\\n&&&&B&=&100-40 \\\\\n&&&&B&=&60 \\text{ cc}\n\\end{array}[\/latex]<\/li>\n \t
  16. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    G21<\/sub><\/th>\nG21<\/sub><\/td>\n0.21<\/td>\n0.21 (G21<\/sub>)<\/td>\n<\/tr>\n
    G15<\/sub><\/th>\n600 \u2212 G21<\/sub><\/td>\n0.15<\/td>\n0.15 (600 \u2212 G21<\/sub>)<\/td>\n<\/tr>\n
    G19<\/sub><\/th>\n600<\/td>\n0.19<\/td>\n0.19 (600)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrrrl}\n0.21G_{21}&+&0.15(600&-&G_{21})&=&0.19(600) \\\\\n0.21G_{21}&+&90&-&0.15G_{21}&=&114 \\\\\n&-&90&&&=&-90 \\\\\n\\hline\n&&&&\\dfrac{0.06G_{21}}{0.06}&=&\\dfrac{24}{0.06} \\\\ \\\\\n&&&&G_{21}&=&400 \\\\\n&&&&G_{15}&=&600-400 \\\\\n&&&&G_{15}&=&200\n\\end{array}[\/latex]<\/li>\n \t
  17. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    C40<\/sub><\/th>\nC40<\/sub><\/td>\n0.40<\/td>\n0.40C40<\/sub><\/td>\n<\/tr>\n
    C30<\/sub><\/th>\n80 \u2212 C40<\/sub><\/td>\n0.30<\/td>\n0.30 (80 \u2212 C40<\/sub>)<\/td>\n<\/tr>\n
    C32<\/sub><\/th>\n80<\/td>\n0.32<\/td>\n0.32 (80)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrrrl}\n0.40C_{40}&+&0.30(80&-&C_{40})&=&0.32(80) \\\\\n0.40C_{40}&+&24&-&0.30C_{40}&=&\\phantom{-}25.6 \\\\\n&-&24&&&=&-24 \\\\\n\\hline\n&&&&\\dfrac{0.10C_{40}}{0.10}&=&\\dfrac{1.6}{1.0} \\\\ \\\\\n&&&&C_{40}&=&16 \\\\\n&&&&C_{30}&=&80-16 \\\\\n&&&&C_{30}&=&64\n\\end{array}[\/latex]<\/li>\n \t
  18. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    A<\/th>\n3.75<\/td>\n0.40<\/td>\n0.40 (3.75)<\/td>\n<\/tr>\n
    F<\/th>\n[latex]x[\/latex]<\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n
    P<\/th>\n[latex]x+3.75[\/latex]<\/td>\n0.06<\/td>\n[latex]0.06(x+3.75)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rlllr}\n0.40(3.75)&=&0.06(x&+&3.75) \\\\\n1.5\\phantom{00}&=&0.06x&+&\\phantom{-}0.225 \\\\\n-0.225&&&&-0.225 \\\\\n\\hline\n\\dfrac{1.275}{0.06}&=&\\dfrac{0.06x}{0.06}&& \\\\ \\\\\nx&=&21.25&& \\\\\n\\end{array}[\/latex]<\/li>\n \t
  19. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    A70<\/sub><\/th>\n[latex]20-x[\/latex]<\/td>\n0.70<\/td>\n[latex]0.70(20-x)[\/latex]<\/td>\n<\/tr>\n
    W<\/th>\n[latex]x[\/latex]<\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n
    A18<\/sub><\/th>\n20<\/td>\n0.18<\/td>\n0.18 (20)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrcrl}\n0.70(20&-&x)&=&0.18(20) \\\\\n\\phantom{-}14&-&0.7x&=&\\phantom{-0}3.6 \\\\\n-14&&&&-14.0 \\\\\n\\hline\n&&\\dfrac{-0.7x}{-0.7}&=&\\dfrac{-10.4}{-0.7} \\\\ \\\\\n&&x&=&14.86 \\text{ L of water}\\\\\n0.70(20&-&14.86)&=&\\phantom{0}5.14 \\text{ L of } 70\\%\n\\end{array}[\/latex]<\/li>\n \t
  20. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    W<\/th>\n[latex]x[\/latex]<\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n
    A100<\/sub><\/th>\n50<\/td>\n1.00<\/td>\n1.00 (50)<\/td>\n<\/tr>\n
    A40<\/sub><\/th>\n[latex]x+50[\/latex]<\/td>\n0.40<\/td>\n[latex]0.40(x+50)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrlll}\n1.00(50)&=&0.40(x&+&50) \\\\\n50&=&0.40x&+&20 \\\\\n-20&=&&-&20 \\\\\n\\hline\n\\dfrac{30}{0.40}&=&\\dfrac{0.40x}{0.40}&& \\\\ \\\\\nx&=&75 \\text{ mL}&&\n\\end{array}[\/latex]<\/li>\n \t
  21. \n\n\n\n\n\n\n
    Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
    W<\/th>\n[latex]x[\/latex]<\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n
    S12<\/sub><\/th>\n50<\/td>\n0.12<\/td>\n0.12 (50)<\/td>\n<\/tr>\n
    S15<\/sub><\/th>\n[latex]50-x[\/latex]<\/td>\n0.15<\/td>\n[latex]0.15(50-x)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}{rrrrr}\n0.12(50)&=&0.15(50&-&x) \\\\\n6.0&=&7.5&-&0.15x \\\\\n-7.5&&-7.5&& \\\\\n\\hline\n\\dfrac{-1.5}{-0.15}&=&\\dfrac{-0.15x}{-0.15}&& \\\\ \\\\\nx&=&10 \\text{ L}&&\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      S40<\/sub><\/th>\n8000<\/td>\n0.40<\/td>\n0.40 (8000)<\/td>\n<\/tr>\n
      W<\/th>\n[latex]x[\/latex]<\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n
      S30<\/sub><\/th>\n[latex]x+8000[\/latex]<\/td>\n0.30<\/td>\n[latex]0.30(x+8000)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]0.40(8000)=0.30(x+8000)[\/latex]<\/li>\n

    2. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      A100<\/sub><\/th>\n[latex]x[\/latex]<\/td>\n1.00<\/td>\n[latex]1.00x[\/latex]<\/td>\n<\/tr>\n
      A30<\/sub><\/th>\n5<\/td>\n0.30<\/td>\n0.30 (5)<\/td>\n<\/tr>\n
      A50<\/sub><\/th>\n[latex]x+5[\/latex]<\/td>\n0.50<\/td>\n[latex]0.50(x+5)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]1.00x+0.30(5)=0.50(x+5)[\/latex]<\/li>\n

    3. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      S10<\/sub><\/th>\n12<\/td>\n0.10<\/td>\n0.10 (12)<\/td>\n<\/tr>\n
      S3<\/sub><\/th>\n[latex]x[\/latex]<\/td>\n0.03<\/td>\n[latex]0.03 (x)[\/latex]<\/td>\n<\/tr>\n
      S5<\/sub><\/th>\n[latex]x+12[\/latex]<\/td>\n0.05<\/td>\n[latex]0.05(x+12)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]0.10(12)+0.03(x)=0.05(x+12)[\/latex]<\/li>\n

    4. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      A100<\/sub><\/th>\n[latex]x[\/latex]<\/td>\n1.00<\/td>\n[latex]1.00x[\/latex]<\/td>\n<\/tr>\n
      A14<\/sub><\/th>\n24<\/td>\n0.14<\/td>\n0.14 (24)<\/td>\n<\/tr>\n
      A20<\/sub><\/th>\n[latex]x+24[\/latex]<\/td>\n0.20<\/td>\n[latex]0.20(x+24)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]1.00x+0.14(24)=0.20(x+24)[\/latex]<\/li>\n

    5. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      B<\/th>\n[latex]x[\/latex]<\/td>\n1.60<\/td>\n[latex]1.60x[\/latex]<\/td>\n<\/tr>\n
      Mag<\/th>\n18<\/td>\n2.50<\/td>\n2.50 (18)<\/td>\n<\/tr>\n
      Mix<\/th>\n[latex]x+18[\/latex]<\/td>\n1.90<\/td>\n[latex]1.90(x+18)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]1.60x+2.50(18)=1.90(x+18)[\/latex]<\/li>\n

    6. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      A100<\/sub><\/th>\n[latex]x[\/latex]<\/td>\n1.00<\/td>\n[latex]1.00x[\/latex]<\/td>\n<\/tr>\n
      A20<\/sub><\/th>\n40<\/td>\n0.20<\/td>\n0.20 (40)<\/td>\n<\/tr>\n
      A36<\/sub><\/th>\n[latex]x+40[\/latex]<\/td>\n0.36<\/td>\n[latex]0.36(x+40)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]x+0.20(40)=0.36(x+40)[\/latex]<\/li>\n

    7. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      O40<\/sub><\/th>\n100<\/td>\n0.40<\/td>\n100 (0.40)<\/td>\n<\/tr>\n
      O100<\/sub><\/th>\n[latex]x[\/latex]<\/td>\n1.00<\/td>\n[latex]x(1.00)[\/latex]<\/td>\n<\/tr>\n
      O50<\/sub><\/th>\n[latex]100+x[\/latex]<\/td>\n0.50<\/td>\n[latex](100+x)(0.50)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]100(0.40)+x=(100+x)(0.50)[\/latex]<\/li>\n

    8. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      P220<\/sub><\/th>\n20<\/td>\n220<\/td>\n220 (20)<\/td>\n<\/tr>\n
      P400<\/sub><\/th>\n[latex]x[\/latex]<\/td>\n400<\/td>\n[latex]400(x)[\/latex]<\/td>\n<\/tr>\n
      P300<\/sub><\/th>\n[latex]x+20[\/latex]<\/td>\n300<\/td>\n[latex]300(x+20)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]220(20)+400x=300(x+20)[\/latex]<\/li>\n

    9. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      T4.20<\/sub><\/th>\n[latex]x[\/latex]<\/td>\n4.20<\/td>\n[latex]4.20(x)[\/latex]<\/td>\n<\/tr>\n
      T2.25<\/sub><\/th>\n12<\/td>\n2.25<\/td>\n2.25 (12)<\/td>\n<\/tr>\n
      T3.40<\/sub><\/th>\n[latex]x+12[\/latex]<\/td>\n3.40<\/td>\n[latex]3.40(x+12)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]4.20x+2.25(12)=3.40(x+12)[\/latex]<\/li>\n

    10. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      S80<\/sub><\/th>\n[latex]x[\/latex]<\/td>\n80<\/td>\n[latex]80(x)[\/latex]<\/td>\n<\/tr>\n
      S25<\/sub><\/th>\n6<\/td>\n25<\/td>\n25 (6)<\/td>\n<\/tr>\n
      S36<\/sub><\/th>\n[latex]x+6[\/latex]<\/td>\n36<\/td>\n[latex]36(x+6)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]\\begin{array}{rrrrrrr} 80x&+&25(6)&=&36(x&+&6) \\\\ 80x&+&150&=&36x&+&216 \\\\ -36x&-&150&&-36x&-&150 \\\\ \\hline &&\\dfrac{44x}{44}&=&\\dfrac{66}{44}&& \\\\ \\\\ &&x&=&\\dfrac{3}{2}&\\text{ or }&1.5 \\text{ L} \\end{array}[\/latex]<\/li>\n

    11. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      C<\/th>\n[latex]x[\/latex]<\/td>\n7.50<\/td>\n[latex]7.50(x)[\/latex]<\/td>\n<\/tr>\n
      J<\/th>\n24<\/td>\n3.25<\/td>\n3.25 (24)<\/td>\n<\/tr>\n
      M<\/th>\n[latex]x+24[\/latex]<\/td>\n4.50<\/td>\n[latex]4.50(x+24)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]\\begin{array}{rrrrrrr} 7.50x&+&3.25(24)&=&4.50(x&+&24) \\\\ 7.50x&+&78&=&4.50x&+&108 \\\\ -4.50x&-&78&&-4.50x&-&78 \\\\ \\hline &&\\dfrac{3.00x}{3.00}&=&\\dfrac{30}{3.00}&& \\\\ \\\\ &&x&=&10 \\text{ kg}&& \\end{array}[\/latex]<\/li>\n

    12. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      S<\/th>\n[latex]x[\/latex]<\/td>\n7.00<\/td>\n[latex]7.00(x)[\/latex]<\/td>\n<\/tr>\n
      A<\/th>\n20<\/td>\n3.50<\/td>\n3.50 (20)<\/td>\n<\/tr>\n
      F<\/th>\n[latex]x+20[\/latex]<\/td>\n4.50<\/td>\n[latex]4.50(x+20)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]\\begin{array}{rrrrrrr} 7.00(x)&+&3.50(20)&=&4.50(x&+&20) \\\\ 7.00x&+&70&=&4.50x&+&90 \\\\ -4.50x&-&70&&-4.50x&-&70 \\\\ \\hline &&\\dfrac{2.5x}{2.5}&=&\\dfrac{20}{2.5}&& \\\\ \\\\ &&x&=&8&& \\end{array}[\/latex]<\/li>\n

    13. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      C1.8<\/sub><\/th>\nC1.8<\/sub><\/td>\n1.80<\/td>\n1.80 (C1.8<\/sub>)<\/td>\n<\/tr>\n
      C3.0<\/sub><\/th>\n15 \u2212 C1.8<\/sub><\/td>\n3.00<\/td>\n3.00 (15 \u2212 C1.8<\/sub>)<\/td>\n<\/tr>\n
      C2.2<\/sub><\/th>\n15<\/td>\n2.20<\/td>\n2.20 (15)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]\\begin{array}{rrrrrrl} 1.80C_{1.8}&+&3.00(15&-&C_{1.8})&=&2.20(15) \\\\ 1.80C_{1.8}&+&45&-&3C_{1.8}&=&\\phantom{-}33 \\\\ &-&45&&&&-45 \\\\ \\hline &&&&\\dfrac{-1.2C_{1.8}}{-1.2}&=&\\dfrac{-12}{-1.2} \\\\ \\\\ &&&&C_{1.8}&=&10 \\\\ &&&&C_{3.0}&=&15-10 \\\\ &&&&C_{3.0}&=&5 \\end{array}[\/latex]<\/li>\n

    14. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      M10<\/sub><\/th>\n100 \u2212 C<\/td>\n0.10<\/td>\n0.10 (100 \u2212 C)<\/td>\n<\/tr>\n
      C<\/th>\nC<\/td>\n0.60<\/td>\n0.60 (C)<\/td>\n<\/tr>\n
      M45<\/sub><\/th>\n100<\/td>\n0.45<\/td>\n0.45 (100)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]\\begin{array}{rrrrrrl} 0.10(100&-&C)&+&0.60(C)&=&0.45(100) \\\\ 10&-&0.10C&+&0.60C&=&\\phantom{-}45 \\\\ -10&&&&&&-10 \\\\ \\hline &&&&\\dfrac{0.50C}{0.50}&=&\\dfrac{35}{0.50} \\\\ \\\\ &&&&C&=&70 \\\\ &&&&M_{10}&=&100-70 \\\\ &&&&M_{10}&=&30 \\end{array}[\/latex]<\/li>\n

    15. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      A<\/th>\nA<\/td>\n0.50<\/td>\n0.50A<\/td>\n<\/tr>\n
      B<\/th>\n100 cc \u2212 A<\/td>\n0.80<\/td>\n0.80 (100 \u2212 A)<\/td>\n<\/tr>\n
      Mix<\/th>\n100 cc<\/td>\n0.68<\/td>\n0.68 (100)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]\\begin{array}{rrrrrrl} 0.50A&+&0.80(100&-&A)&=&0.68(100) \\\\ 0.50A&+&80&-&0.80A&=&\\phantom{-}68 \\\\ &-&80&&&=&-80 \\\\ \\hline &&&&\\dfrac{-0.30A}{-0.30}&=&\\dfrac{-12}{-0.30} \\\\ \\\\ &&&&A&=&40 \\text{ cc} \\\\ &&&&B&=&100-40 \\\\ &&&&B&=&60 \\text{ cc} \\end{array}[\/latex]<\/li>\n

    16. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      G21<\/sub><\/th>\nG21<\/sub><\/td>\n0.21<\/td>\n0.21 (G21<\/sub>)<\/td>\n<\/tr>\n
      G15<\/sub><\/th>\n600 \u2212 G21<\/sub><\/td>\n0.15<\/td>\n0.15 (600 \u2212 G21<\/sub>)<\/td>\n<\/tr>\n
      G19<\/sub><\/th>\n600<\/td>\n0.19<\/td>\n0.19 (600)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]\\begin{array}{rrrrrrl} 0.21G_{21}&+&0.15(600&-&G_{21})&=&0.19(600) \\\\ 0.21G_{21}&+&90&-&0.15G_{21}&=&114 \\\\ &-&90&&&=&-90 \\\\ \\hline &&&&\\dfrac{0.06G_{21}}{0.06}&=&\\dfrac{24}{0.06} \\\\ \\\\ &&&&G_{21}&=&400 \\\\ &&&&G_{15}&=&600-400 \\\\ &&&&G_{15}&=&200 \\end{array}[\/latex]<\/li>\n

    17. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      C40<\/sub><\/th>\nC40<\/sub><\/td>\n0.40<\/td>\n0.40C40<\/sub><\/td>\n<\/tr>\n
      C30<\/sub><\/th>\n80 \u2212 C40<\/sub><\/td>\n0.30<\/td>\n0.30 (80 \u2212 C40<\/sub>)<\/td>\n<\/tr>\n
      C32<\/sub><\/th>\n80<\/td>\n0.32<\/td>\n0.32 (80)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]\\begin{array}{rrrrrrl} 0.40C_{40}&+&0.30(80&-&C_{40})&=&0.32(80) \\\\ 0.40C_{40}&+&24&-&0.30C_{40}&=&\\phantom{-}25.6 \\\\ &-&24&&&=&-24 \\\\ \\hline &&&&\\dfrac{0.10C_{40}}{0.10}&=&\\dfrac{1.6}{1.0} \\\\ \\\\ &&&&C_{40}&=&16 \\\\ &&&&C_{30}&=&80-16 \\\\ &&&&C_{30}&=&64 \\end{array}[\/latex]<\/li>\n

    18. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      A<\/th>\n3.75<\/td>\n0.40<\/td>\n0.40 (3.75)<\/td>\n<\/tr>\n
      F<\/th>\n[latex]x[\/latex]<\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n
      P<\/th>\n[latex]x+3.75[\/latex]<\/td>\n0.06<\/td>\n[latex]0.06(x+3.75)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]\\begin{array}{rlllr} 0.40(3.75)&=&0.06(x&+&3.75) \\\\ 1.5\\phantom{00}&=&0.06x&+&\\phantom{-}0.225 \\\\ -0.225&&&&-0.225 \\\\ \\hline \\dfrac{1.275}{0.06}&=&\\dfrac{0.06x}{0.06}&& \\\\ \\\\ x&=&21.25&& \\\\ \\end{array}[\/latex]<\/li>\n

    19. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      A70<\/sub><\/th>\n[latex]20-x[\/latex]<\/td>\n0.70<\/td>\n[latex]0.70(20-x)[\/latex]<\/td>\n<\/tr>\n
      W<\/th>\n[latex]x[\/latex]<\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n
      A18<\/sub><\/th>\n20<\/td>\n0.18<\/td>\n0.18 (20)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]\\begin{array}{rrcrl} 0.70(20&-&x)&=&0.18(20) \\\\ \\phantom{-}14&-&0.7x&=&\\phantom{-0}3.6 \\\\ -14&&&&-14.0 \\\\ \\hline &&\\dfrac{-0.7x}{-0.7}&=&\\dfrac{-10.4}{-0.7} \\\\ \\\\ &&x&=&14.86 \\text{ L of water}\\\\ 0.70(20&-&14.86)&=&\\phantom{0}5.14 \\text{ L of } 70\\% \\end{array}[\/latex]<\/li>\n

    20. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      W<\/th>\n[latex]x[\/latex]<\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n
      A100<\/sub><\/th>\n50<\/td>\n1.00<\/td>\n1.00 (50)<\/td>\n<\/tr>\n
      A40<\/sub><\/th>\n[latex]x+50[\/latex]<\/td>\n0.40<\/td>\n[latex]0.40(x+50)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]\\begin{array}{rrlll} 1.00(50)&=&0.40(x&+&50) \\\\ 50&=&0.40x&+&20 \\\\ -20&=&&-&20 \\\\ \\hline \\dfrac{30}{0.40}&=&\\dfrac{0.40x}{0.40}&& \\\\ \\\\ x&=&75 \\text{ mL}&& \\end{array}[\/latex]<\/li>\n

    21. \n\n\n\n\n\n\n
      Name<\/th>\nAmount<\/th>\nValue<\/th>\nEquation<\/th>\n<\/tr>\n
      W<\/th>\n[latex]x[\/latex]<\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n
      S12<\/sub><\/th>\n50<\/td>\n0.12<\/td>\n0.12 (50)<\/td>\n<\/tr>\n
      S15<\/sub><\/th>\n[latex]50-x[\/latex]<\/td>\n0.15<\/td>\n[latex]0.15(50-x)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      [latex]\\begin{array}{rrrrr} 0.12(50)&=&0.15(50&-&x) \\\\ 6.0&=&7.5&-&0.15x \\\\ -7.5&&-7.5&& \\\\ \\hline \\dfrac{-1.5}{-0.15}&=&\\dfrac{-0.15x}{-0.15}&& \\\\ \\\\ x&=&10 \\text{ L}&& \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":56,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-1891","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1891","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1891\/revisions"}],"predecessor-version":[{"id":1892,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1891\/revisions\/1892"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1891\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1891"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1891"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1891"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1891"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}