SOLUTION: A chemist has one solution that is 40% alcohol and another that is 55% alcohol. How much of each must she use to make 15 liters of solution that is 50% alcohol?

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Question 306509: A chemist has one solution that is 40% alcohol and another that is 55% alcohol. How much of each must she use to make 15 liters of solution that is 50% alcohol?
Answer by dabanfield(803) (Show Source):
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A chemist has one solution that is 40% alcohol and another that is 55% alcohol. How much of each must she use to make 15 liters of solution that is 50% alcohol?
Let x be the amount of 40% alcohol and y the amount of 55% alcohol. Then we have:
1.) x + y = 15 and
2.) .40x + .55y = .50*15
From 1.) we know that x = 15-y. Substituting 15-y for x in 2.) gives us:
.40*(15-y) + .55*y = 7.5
6 - .4y + .55y = 7.5
.15y = 1.5
y = 10
Substituting 10 for y in equation 1.) we have x + 10 = 15, so x =5.