2011 AIME II Problems/Problem 1

Problem:

Gary purchased a large bevarage, but only drank m/n of it, where m and n are relatively prime positive integers. If he had purchased half as m uch and drank twice as much, he would have wasted only 2/9 as much bevarage. Find m+n.

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Solution:

Set up a system of equations, which I will leave to somebody with more free time, and you get that m=5 and n=32. m+n=37