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?

1 Answer
Oct 15, 2015

Answer:

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.