Difference between revisions of "2011 AIME II Problems/Problem 1"
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Revision as of 22:37, 23 November 2024
Contents
Problem
Gary purchased a large beverage, but only drank of it, where
and
are relatively prime positive integers. If he had purchased half as much and drunk twice as much, he would have wasted only
as much beverage. Find
.
Solution
Let be the fraction consumed, then
is the fraction wasted. We have
, or
, or
or
. Therefore,
.
Solution 2
~idk123456
See also
2011 AIME II (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.