Math CentralQuandaries & Queries


Question from Leeanne, a student:

here is my question:
a chemist has 200 liters of solution that is 5% acid. how many liters of water
(0% acid) must he add to make a solution that is 4% acid?

Hi Leeanne.

The concentration times the volume of a mixture tells you how much of the active ingredient is in there.

So the chemist starts with 200x(5%) = 10 liters of the acid itself.

The question is this:

10 liters is 4% of what number?

10 liters = 4% of x.

10 = 0.04(x)

10 / 0.04 = 0.04x / 0.04
x = 10 / 0.04
x = 1000 / 4
x = 250 liters.

So the total volume of the 4% solution the chemist makes is 250 liters. That's 50 liters more than she started with. So she added 50 liters of water to the original solution.

Stephen La Rocque

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