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 "m"+"n".
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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''.
  
 
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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 "m"=5 and "n"=32. "m"+"n"=37
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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''=37

Revision as of 21:05, 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