Answer
5 gallons of 10% and 15 gallons of 20% are needed.
Work Step by Step
$17.5\%$ is 3/4 of the way between 20 percent and 10 percent. Thus, of the 20 gallons, 3/4 must be the 20 percent solution. Thus:
$$ Amount \ of \ 20\%: \\ = (20 \ gallons)(.75) \\ = 15\ gallons $$
So:
$$ Amount \ of \ 10\%: \\ = (20 \ gallons)(.25) \\ = 5\ gallons $$
