SOLUTION: A chemist has two alcohol solutions, one is 20% and one is 50% alcohol solution. He needs 12 liters of a solution that is 45% alcohol, how much of each does he mix?

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Question 441219: A chemist has two alcohol solutions, one is 20% and one is 50% alcohol solution. He needs 12 liters of a solution that is 45% alcohol, how much of each does he mix?
Found 2 solutions by rwm, stanbon:
Answer by rwm(914) About Me  (Show Source):
You can put this solution on YOUR website!
x+y=12
.2x+.5y=.45*12
x=2 y=10

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A chemist has two alcohol solutions, one is 20% and one is 50% alcohol solution. He needs 12 liters of a solution that is 45% alcohol, how much of each does he mix?
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Equations:
Quantity Eq.::: t + f = 12 liters
Alcohol Eq::: 0.20t+.50f = 0.45(12)
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Multiply thru 1st by 20
Multiply thru 2nd by 100
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20t + 20f = 20*12
20t + 50f = 45*12
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Subtract and solve for "f":
30f = 25*12
f = 10 liters (amt. of 50% solution needed)
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Solve for "t":
t + f = 12
t = 12-10
t = 2 liters (amt. of 20% solution needed)
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Cheers,
Stan H.
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