Let x = the required number of gallons of 5% acid solution.

You can write the equation from the problem description but first convert the percentages to their decimal equivalents.

5% of x + 10% of 5 = 7% of (x+5)

0.05(x) + 0.1(5) = 0.07(x+5)

Simplify and solve for x.

0.05x + 0.5 = 0.35 + 0.07x Subtract 0.05x from both sides.

0.5 = 0.35+0.02x Subtract 0.35 from both sides.

0.15 = 0.02x Finally, divide both sides by 0.02

x = 7.5 

You will need to add 7.5 gallons of 5% acid solution to 5 gallons of 10% acid solution to obtain 12.5 gallons of 7% acid solution.