SOLUTION: how many liters of a 12% alcohol solution must be added to 15 liters of a 5% alcohol solution to get a mixture that is 8% alcohol?

Question 1136822: how many liters of a 12% alcohol solution must be added to 15 liters of a 5% alcohol solution to get a mixture that is 8% alcohol?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let x be the number of liters needed to add to the 12% solution
:
we have three relations, the third relation is the mixture
:
1) x * 0.12 = 0.12x
:
2) 15 * 0.05 = 0.75
:
3) (x+15) * 0.08 = 0.08(x+15)
:
0.12x +0.75 = 0.08(x+15)
:
0.12x +0.75 = 0.08x +1.20
:
0.04x = 0.45
:
x = 11.25
:
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11.25 liters of the 12% solution is necessary
:
check answer
:
0.12(11.25) +0.75 = 0.08(11.25) +1.20
:
1.35 +0.75 = 0.90 +1.20
:
2.1 = 2.1
:
also
:
(11.25 + 15) * 0.08 = 2.1
:
answer checks
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