A 20-gallon salt-water solution contains 15% pure salt. How much pure water should be added to it to produce a 10% solution?

15% of 20 gal = 0.15 * 20 gal = 3 gal, so the solution contains 3 gal of salt.

If we add x gal of water to the solution, we end up with (20 + x) gal of solution. We want the new mixture to have a concentration of 10%, or

10% of (20 + x) gal = 0.1 * (20 + x) gal = 2 + 0.1x gal

of salt.

The amount of salt in the tank hasn't changed. Solve for x:

2 + 0.1x = 3

0.1x = 1

x = 10 gal