Answer Key 6.8
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Name Amount Value Equation S40 8000 0.40 0.40 (8000) W [latex]x[/latex] 0 0 S30 [latex]x+8000[/latex] 0.30 [latex]0.30(x+8000)[/latex] [latex]0.40(8000)=0.30(x+8000)[/latex]
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Name Amount Value Equation A100 [latex]x[/latex] 1.00 [latex]1.00x[/latex] A30 5 0.30 0.30 (5) A50 [latex]x+5[/latex] 0.50 [latex]0.50(x+5)[/latex] [latex]1.00x+0.30(5)=0.50(x+5)[/latex]
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Name Amount Value Equation S10 12 0.10 0.10 (12) S3 [latex]x[/latex] 0.03 [latex]0.03 (x)[/latex] S5 [latex]x+12[/latex] 0.05 [latex]0.05(x+12)[/latex] [latex]0.10(12)+0.03(x)=0.05(x+12)[/latex]
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Name Amount Value Equation A100 [latex]x[/latex] 1.00 [latex]1.00x[/latex] A14 24 0.14 0.14 (24) A20 [latex]x+24[/latex] 0.20 [latex]0.20(x+24)[/latex] [latex]1.00x+0.14(24)=0.20(x+24)[/latex]
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Name Amount Value Equation B [latex]x[/latex] 1.60 [latex]1.60x[/latex] Mag 18 2.50 2.50 (18) Mix [latex]x+18[/latex] 1.90 [latex]1.90(x+18)[/latex] [latex]1.60x+2.50(18)=1.90(x+18)[/latex]
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Name Amount Value Equation A100 [latex]x[/latex] 1.00 [latex]1.00x[/latex] A20 40 0.20 0.20 (40) A36 [latex]x+40[/latex] 0.36 [latex]0.36(x+40)[/latex] [latex]x+0.20(40)=0.36(x+40)[/latex]
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Name Amount Value Equation O40 100 0.40 100 (0.40) O100 [latex]x[/latex] 1.00 [latex]x(1.00)[/latex] O50 [latex]100+x[/latex] 0.50 [latex](100+x)(0.50)[/latex] [latex]100(0.40)+x=(100+x)(0.50)[/latex]
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Name Amount Value Equation P220 20 220 220 (20) P400 [latex]x[/latex] 400 [latex]400(x)[/latex] P300 [latex]x+20[/latex] 300 [latex]300(x+20)[/latex] [latex]220(20)+400x=300(x+20)[/latex]
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Name Amount Value Equation T4.20 [latex]x[/latex] 4.20 [latex]4.20(x)[/latex] T2.25 12 2.25 2.25 (12) T3.40 [latex]x+12[/latex] 3.40 [latex]3.40(x+12)[/latex] [latex]4.20x+2.25(12)=3.40(x+12)[/latex]
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Name Amount Value Equation S80 [latex]x[/latex] 80 [latex]80(x)[/latex] S25 6 25 25 (6) S36 [latex]x+6[/latex] 36 [latex]36(x+6)[/latex] [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]
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Name Amount Value Equation C [latex]x[/latex] 7.50 [latex]7.50(x)[/latex] J 24 3.25 3.25 (24) M [latex]x+24[/latex] 4.50 [latex]4.50(x+24)[/latex] [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]
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Name Amount Value Equation S [latex]x[/latex] 7.00 [latex]7.00(x)[/latex] A 20 3.50 3.50 (20) F [latex]x+20[/latex] 4.50 [latex]4.50(x+20)[/latex] [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]
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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) [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]
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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) [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]
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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) [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]
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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) [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]
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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) [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]
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Name Amount Value Equation A 3.75 0.40 0.40 (3.75) F [latex]x[/latex] 0 0 P [latex]x+3.75[/latex] 0.06 [latex]0.06(x+3.75)[/latex] [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]
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Name Amount Value Equation A70 [latex]20-x[/latex] 0.70 [latex]0.70(20-x)[/latex] W [latex]x[/latex] 0 0 A18 20 0.18 0.18 (20) [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]
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Name Amount Value Equation W [latex]x[/latex] 0 0 A100 50 1.00 1.00 (50) A40 [latex]x+50[/latex] 0.40 [latex]0.40(x+50)[/latex] [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]
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Name Amount Value Equation W [latex]x[/latex] 0 0 S12 50 0.12 0.12 (50) S15 [latex]50-x[/latex] 0.15 [latex]0.15(50-x)[/latex] [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]
