Difference between revisions of "2011 AIME II Problems/Problem 1"
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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". | 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: | ||
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| + | 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"=\boxed{37} | ||
Revision as of 22:04, 30 March 2011
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".
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"=\boxed{37}
