Question

How much of a 60% acid solution must be mixed with 50 gallons of a 24% acid solution to obtain a solution that is 50% acid?

a.

130 gal

c.

13 gal
b.

125 gal

d.

None of these

Answer 1

A. 130 gal

Explanation:

Answer 2

x gallons of a 60% acid solution contains 60%×x=0.6x gallons of acid.
50 gallons of a 24% acid solution contains 24%×50=0.24×50=12 gallons of acid.

After mixing, there will be x+50 gallons of a solution, and 0.6x+12 gallons of acid. The concentration must be 50%, so the volume of acid divided by the volume of the solution is 50%, or 0.5.


`(0.6x+12)/(x+50)=0.5 \\ 0.6x+12=0.5(x+50) \\ 0.6x+12=0.5x+25 \\ 0.6x-0.5x=25-12 \\ 0.1x=13 \\ 0.1x * 10=13 * 10 \\ x=130`

The answer is A. 130 gallons.