Problem:
Before starting to paint, Bill had ounces of blue paint, ounces of red paint, and ounces of white paint. Bill painted four equally sized stripes on a wall, making a blue stripe, a red stripe, a white stripe, and a pink stripe. Pink is a mixture of red and white, not necessarily in equal amounts. When Bill finished, he had equal amounts of blue, red, and white paint left. Find the total number of ounces of paint Bill had left.
Solution:
Bill must have used more ounces of red paint than blue paint and more ounces of white paint than blue paint. It follows that it took ounces of paint to paint the pink stripe, and therefore ounces to paint each stripe. Thus ounces of blue paint were left, and a total of ounces of paint.
The problems on this page are the property of the MAA's American Mathematics Competitions