Question

A scientist needs 10 liters of a 20% acid solution for an experiment, but she has only a 5% solution and a 40% solution. To the nearest tenth of a liter, about how many liters of the 5% and the 40% solutions should she mix to get the solution she needs?

Answer 1

In this question, you want to make 10 liters 20% concentration solution by mixing 5% and 40% concentration. There should be multiple answers to this question. Assuming that the total volume of 5% and 40% solution equal to 10L(no solution wasted), then you can determine the volume of solution needed. The formula should be:

if x would be the of volume 40% solution, then the volume of 5% would be:
10 L= 40% solution volume+ 5% solution volume
10 L= x + 5% solution volume
5% solution volume= 10l-x

Then the volume calculation would be:
volume20%*concentration20%= volume40%*concentration40% + volume5%*concentration5%
10 liter * 20%= x liter*40% + (10- x) liter*5%
10l * 20%= x liter * 35% + 10 liter*5%
x liter *35 = 10l * 20 - 10l *5= 10l*15
x liter = 10l *15/35= 4.28 L= 4.3L

The volume of 40% solution= 4.3L
The volume of 5% solution= 10L- 4.3L= 5.7L