Maths Olympiad Prep

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Problem 341

Algebra Difficulty 2.3 Find the answer CEMC Cayley

What fraction of the entire wall is painted red if Matilda paints half of her section red and Ellie paints one third of her section red?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

Matilda and Ellie each take 12\frac{1}{2} of the wall. Matilda paints 12\frac{1}{2} of her half, or 12×12=14\frac{1}{2} \times \frac{1}{2} = \frac{1}{4} of the entire wall. Ellie paints 13\frac{1}{3} of her half, or 13×12=16\frac{1}{3} \times \frac{1}{2} = \frac{1}{6} of the entire wall. Therefore, 14+16=312+212=512\frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12} of the wall is painted red.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.