2007 AMC 8 Problems/Problem 20

Regular season wins and losses are related in two ways:

wins / (wins + losses) = 0.45 wins + 6 = losses + 2

So wins + 4 = losses or wins = losses - 4

so wins / (wins + wins + 4) = 0.45 or 9/20

so 20 * wins = 18 * wins + 9 * 4

so wins = 9 * 2 = 18

so losses = 22

so regular season games = 40.

So the total number of games is 40 + 6 + 2 = 48.