Math CentralQuandaries & Queries


Question from MJ, a student:

How many liters of pure acetic acid must be mixed with 3 liters of a 30% acetic acid to obtain a mixture of 65%?


You ned to think carefully about what this question is asking and develop an algebraic expression.

The original solution is 30 liters of a 30% acetic acid solution so in this solution is $0.30 \times 3 = 0.9$ liters of pure acid. You are going to add $x$ liters of pure acid so the volume of the resulting mixture will be $x + 3$ liters. 65% of this mixture is to be pure acid so that's $0.65 \times (x + 3)$ liters of pure acid.

But you know how much pure acid is in the mixture, $x$ liters you added plus $0.9$ liters that was already there

Can you complete the problem now?

Make sure you verify your answer.

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