Difference between revisions of "2011 AIME II Problems/Problem 1"
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Problem: | 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 | + | 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: | Solution: | ||
| − | Set up a system of equations, which I will leave to somebody with more free time, and you get that | + | 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 |
Revision as of 22:05, 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=37
