# Suppose you work in a lab and you need a 15% acid solution to conduct a certain test, but your supplier only ships a 10% solution and a 30% solution. You need 10 liters of the 15% acid solution?

Oct 15, 2015

Let's work this out by saying the amount of 10% solution is $x$

#### Explanation:

Then the 30% solution will be $10 - x$

The wanted 15% solution contains $0 , 15 \cdot 10 = 1.5$ of acid.
The 10% solution will provide $0.10 \cdot x$
And the 30% solution will provide $0.30 \cdot \left(10 - x\right)$

So:
$0.10 x + 0.30 \left(10 - x\right) = 1.5 \to$
$0.10 x + 3 - 0.30 x = 1.5 \to$
$3 - 0.20 x = 1.5 \to 1.5 = 0.20 x \to x = 7.5$

You will need 7.5 L of the 10% solution and 2.5 L of the 30%.

Note :
You can do this another way. Between 10% and 30% is a difference of 20. You need to go up from 10% to 15%. This is a difference of 5.

So your mix should contain $\frac{5}{20} = \frac{1}{4}$ of the stronger stuff.