A 20% acid solution is mixed with a 70% acid solution to get 50 liters of a 40% solution.

How much of the 70% solution is used?

Question

A 20% acid solution is mixed with a 70% acid solution to get 50 liters of a 40% solution.

How much of the 70% solution is used?

owlfred · Answer

Let's think in terms of pure acid. I love pure acid.

50 liters of a 40% acid solution contains $50 \times \frac{40}{100} = 20 ~l$ of pure acid. That's a good start. 

Now, let the volume of $20\%$ acid solution be $x$ and the volume of $70\%$ acid solution be $y$.

First of all, mixing those two solutions gives you 50 liters of a solution, meaning that $x+ y = 50$.

Secondly, let's again think in terms of pure acid. If I have $x$ liters of 20% acid solution, then I will have $\frac{20}{100}x$ liters of pure acid. Also, if I have $y$ liters of a 70% acid solution, then I have $\frac{70}{100}y $ liters of pure acid. When I mix those two, I get 20 liters of pure acid. In other words, $\text{pure acid from the first mixture + pure acid from the second mixture}$ is equal to $\text{20 liters of pure acid}$.

Our second equation would then be $\frac{2}{10}x + \frac{7}{10}y = 20$.