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.
\(\frac{0.6x+12}{x+50}=0.5 \\
0.6x+12=0.5(x+50) \\
0.6x+12=0.5x+25 \\
0.6x-0.5x=25-12 \\
0.1x=13 \\
0.1x \times 10=13 \times 10 \\
x=130\)
The answer is A. 130 gallons.
