Difference between revisions of "2011 AMC 12B Problems/Problem 7"
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Revision as of 14:49, 6 March 2011
Problem
Let and be two-digit positive integers with mean . What is the maximum value of the ratio ?
Solution
If and have a mean of , then and . To maximize , we need to maximize and minimize . Since they are both two-digit positive integers, the maximum of is which gives . cannot be decreased because doing so would increase , so this gives the maximum value of , which is