Answer:
<h3>              0.125 galon of 35% acid solution</h3>
Step-by-step explanation:
0.5 gallon of a 10% acid solution 
10%•0.5 = 0.05 gallon of acid in that solution
x gallon of 35% acid solution 
35%•x = 0.35x  gallons of acid in that solution
0.05 + 0.35x  total of gallons of acid in both solutions 
(0.5+x) gallons of 15% acid solution
15%(0.5+x) = 0.15(0.5+x)  gallons of acid in that solution
the amount of gallons of acid didn't change after mixing, so:
0.05 + 0.35x = 0.15(0.5 + x)
0.05 + 0.35x = 0.075 + 0.15x
0.35x - 0.15x = 0.075  - 0.05
0.2x = 0.025
  ×5         ×5  
  x = 0.125