Answer Key 6.8

  1. Name Amount Value Equation
    S40 8000 0.40 0.40 (8000)
    W x 0 0
    S30 x+8000 0.30 0.30(x+8000)

    0.40(8000)=0.30(x+8000)

  2. Name Amount Value Equation
    A100 x 1.00 1.00x
    A30 5 0.30 0.30 (5)
    A50 x+5 0.50 0.50(x+5)

    1.00x+0.30(5)=0.50(x+5)

  3. Name Amount Value Equation
    S10 12 0.10 0.10 (12)
    S3 x 0.03 0.03 (x)
    S5 x+12 0.05 0.05(x+12)

    0.10(12)+0.03(x)=0.05(x+12)

  4. Name Amount Value Equation
    A100 x 1.00 1.00x
    A14 24 0.14 0.14 (24)
    A20 x+24 0.20 0.20(x+24)

    1.00x+0.14(24)=0.20(x+24)

  5. Name Amount Value Equation
    B x 1.60 1.60x
    Mag 18 2.50 2.50 (18)
    Mix x+18 1.90 1.90(x+18)

    1.60x+2.50(18)=1.90(x+18)

  6. Name Amount Value Equation
    A100 x 1.00 1.00x
    A20 40 0.20 0.20 (40)
    A36 x+40 0.36 0.36(x+40)

    x+0.20(40)=0.36(x+40)

  7. Name Amount Value Equation
    O40 100 0.40 100 (0.40)
    O100 x 1.00 x(1.00)
    O50 100+x 0.50 (100+x)(0.50)

    100(0.40)+x=(100+x)(0.50)

  8. Name Amount Value Equation
    P220 20 220 220 (20)
    P400 x 400 400(x)
    P300 x+20 300 300(x+20)

    220(20)+400x=300(x+20)

  9. Name Amount Value Equation
    T4.20 x 4.20 4.20(x)
    T2.25 12 2.25 2.25 (12)
    T3.40 x+12 3.40 3.40(x+12)

    4.20x+2.25(12)=3.40(x+12)

  10. Name Amount Value Equation
    S80 x 80 80(x)
    S25 6 25 25 (6)
    S36 x+6 36 36(x+6)

    \begin{array}{rrrrrrr} 80x&+&25(6)&=&36(x&+&6) \\ 80x&+&150&=&36x&+&216 \\ -36x&-&150&&-36x&-&150 \\ \midrule &&\dfrac{44x}{44}&=&\dfrac{66}{44}&& \\ \\ &&x&=&\dfrac{3}{2}&\text{ or }&1.5 \text{ L} \end{array}

  11. Name Amount Value Equation
    C x 7.50 7.50(x)
    J 24 3.25 3.25 (24)
    M x+24 4.50 4.50(x+24)

    \begin{array}{rrrrrrr} 7.50x&+&3.25(24)&=&4.50(x&+&24) \\ 7.50x&+&78&=&4.50x&+&108 \\ -4.50x&-&78&&-4.50x&-&78 \\ \midrule &&\dfrac{3.00x}{3.00}&=&\dfrac{30}{3.00}&& \\ \\ &&x&=&10 \text{ kg}&& \end{array}

  12. Name Amount Value Equation
    S x 7.00 7.00(x)
    A 20 3.50 3.50 (20)
    F x+20 4.50 4.50(x+20)

    \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 \\ \midrule &&\dfrac{2.5x}{2.5}&=&\dfrac{20}{2.5}&& \\ \\ &&x&=&8&& \end{array}

  13. Name Amount Value Equation
    C1.8 C1.8 1.80 1.80 (C1.8)
    C3.0 15 − C1.8 3.00 3.00 (15 − C1.8)
    C2.2 15 2.20 2.20 (15)

    \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 \\ \midrule &&&&\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}

  14. Name Amount Value Equation
    M10 100 − C 0.10 0.10 (100 − C)
    C C 0.60 0.60 (C)
    M45 100 0.45 0.45 (100)

    \begin{array}{rrrrrrl} 0.10(100&-&C)&+&0.60(C)&=&0.45(100) \\ 10&-&0.10C&+&0.60C&=&\phantom{-}45 \\ -10&&&&&&-10 \\ \midrule &&&&\dfrac{0.50C}{0.50}&=&\dfrac{35}{0.50} \\ \\ &&&&C&=&70 \\ &&&&M_{10}&=&100-70 \\ &&&&M_{10}&=&30 \end{array}

  15. Name Amount Value Equation
    A A 0.50 0.50A
    B 100 cc − A 0.80 0.80 (100 − A)
    Mix 100 cc 0.68 0.68 (100)

    \begin{array}{rrrrrrl} 0.50A&+&0.80(100&-&A)&=&0.68(100) \\ 0.50A&+&80&-&0.80A&=&\phantom{-}68 \\ &-&80&&&=&-80 \\ \midrule &&&&\dfrac{-0.30A}{-0.30}&=&\dfrac{-12}{-0.30} \\ \\ &&&&A&=&40 \text{ cc} \\ &&&&B&=&100-40 \\ &&&&B&=&60 \text{ cc} \end{array}

  16. Name Amount Value Equation
    G21 G21 0.21 0.21 (G21)
    G15 600 − G21 0.15 0.15 (600 − G21)
    G19 600 0.19 0.19 (600)

    \begin{array}{rrrrrrl} 0.21G_{21}&+&0.15(600&-&G_{21})&=&0.19(600) \\ 0.21G_{21}&+&90&-&0.15G_{21}&=&114 \\ &-&90&&&=&-90 \\ \midrule &&&&\dfrac{0.06G_{21}}{0.06}&=&\dfrac{24}{0.06} \\ \\ &&&&G_{21}&=&400 \\ &&&&G_{15}&=&600-400 \\ &&&&G_{15}&=&200 \end{array}

  17. Name Amount Value Equation
    C40 C40 0.40 0.40C40
    C30 80 − C40 0.30 0.30 (80 − C40)
    C32 80 0.32 0.32 (80)

    \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 \\ \midrule &&&&\dfrac{0.10C_{40}}{0.10}&=&\dfrac{1.6}{1.0} \\ \\ &&&&C_{40}&=&16 \\ &&&&C_{30}&=&80-16 \\ &&&&C_{30}&=&64 \end{array}

  18. Name Amount Value Equation
    A 3.75 0.40 0.40 (3.75)
    F x 0 0
    P x+3.75 0.06 0.06(x+3.75)

    \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 \\ \midrule \dfrac{1.275}{0.06}&=&\dfrac{0.06x}{0.06}&& \\ \\ x&=&21.25&& \\ \end{array}

  19. Name Amount Value Equation
    A70 20-x 0.70 0.70(20-x)
    W x 0 0
    A18 20 0.18 0.18 (20)

    \begin{array}{rrcrl} 0.70(20&-&x)&=&0.18(20) \\ \phantom{-}14&-&0.7x&=&\phantom{-0}3.6 \\ -14&&&&-14.0 \\ \midrule &&\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}

  20. Name Amount Value Equation
    W x 0 0
    A100 50 1.00 1.00 (50)
    A40 x+50 0.40 0.40(x+50)

    \begin{array}{rrlll} 1.00(50)&=&0.40(x&+&50) \\ 50&=&0.40x&+&20 \\ -20&=&&-&20 \\ \midrule \dfrac{30}{0.40}&=&\dfrac{0.40x}{0.40}&& \\ \\ x&=&75 \text{ mL}&& \end{array}

  21. Name Amount Value Equation
    W x 0 0
    S12 50 0.12 0.12 (50)
    S15 50-x 0.15 0.15(50-x)

    \begin{array}{rrrrr} 0.12(50)&=&0.15(50&-&x) \\ 6.0&=&7.5&-&0.15x \\ -7.5&&-7.5&& \\ \midrule \dfrac{-1.5}{-0.15}&=&\dfrac{-0.15x}{-0.15}&& \\ \\ x&=&10 \text{ L}&& \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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