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Problem 557

Algebra Difficulty 2.6 Find the answer CEMC Fermat

If $x + 2y = 30$ , what is the value of $\frac{x}{5} + \frac{2y}{3} + \frac{2y}{5} + \frac{x}{3}$ ?

Your answer

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

Official solution

Since $x + 2y = 30$ , then $\frac{x}{5} + \frac{2y}{3} + \frac{2y}{5} + \frac{x}{3} = \frac{x}{5} + \frac{2y}{5} + \frac{x}{3} + \frac{2y}{3} = \frac{1}{5}x + \frac{1}{5}(2y) + \frac{1}{3}x + \frac{1}{3}(2y) = \frac{1}{5}(x + 2y) + \frac{1}{3}(x + 2y) = \frac{1}{5}(30) + \frac{1}{3}(30) = 6 + 10 = 16$

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