Question

A pharmacist has an 18% alcohol solution and a 40% alcohol solution. How much of each should he mix together to make 10 liters of a 20% alcohol solution?

Answer 1

9.091 liters of the 18% alcohol solution, 0.909 liters of the 40% alcohol solution.

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Answer 2

The amount of alcohol is unchanged after adding water. So, if there are x liters of 18% solution, you have

.18x = .12*10
x = 20/3 L of 18% alcohol, and 10/3 L of water

Or, you can consider that you are reducing the concentration by a factor of 2/3, so you must increase the volume by a factor of 3/2. So, the volume v of 18% alcohol can be found by

3/2 v = 10
v = 20/3