1992 AIME Problems/Problem 3
A tennis player computes her win ratio by dividing the number of matches she has won by the total number of matches she has played. At the start of a weekend, her win ratio is exactly . During the weekend, she plays four matches, winning three and losing one. At the end of the weekend, her win ratio is greater than . What's the largest number of matches she could've won before the weekend began?
Let be the number of matches won, so that , and . Cross multiplying, , and . Thus, the answer is .