SOLUTION: 23% solution is added to 17% solution to get 45 gallons of 20% solution. How much of each should be added?

Question 990543: 23% solution is added to 17% solution to get 45 gallons of 20% solution. How much of each should be added?
Found 2 solutions by Boreal, macston:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x=23% solution
45-x=17% solution
.23x+ 0.17(45-x)=45*0.20=9
.23x + 7.65-0.17x=9
0.06x=1.35
x=22.5 gal of 23%
45-x=22.5 gal
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Faster way.
If you mix them 1:1 you get 20%, so it will be half of 45 for each.

Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
.
T=amount of 23% solution; S=amount of 17% solution
.
T+S=45 gallons
S=45 gallons-T
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0.23T+0.17S=0.20(45 gallons)
0.23T+0.17(45gal-T)=9gal
0.23T+7.65gal-0.17T=9gal
0.06T=1.35gal
T=22.5 gallons
ANSWER 1: 22.5 gallons of 23% solution should be added.
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S=45gal-T=45gal-22.5gal=22.5gal
ANSWER 2: 22.5 gallons of 17% solution should be added.
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CHECK:
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0.23T+0.17S=0.20(45 gallons)
0.23(22.5gal)+0.17(22.5gal)=0.20(45gal)
5.175gal+3.825gal=9gal
9gal=9gal

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