Question

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?

Answer 1

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*10=1.5` of acid.
The 10% solution will provide `0.10*x`
And the 30% solution will provide `0.30*(10-x)`

So:
`0.10x+0.30(10-x)=1.5->`
`0.10x+3-0.30x=1.5->`
`3-0.20x=1.5->1.5=0.20x->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 `5/20=1/4` of the stronger stuff.