2007 AMC 8 Problems/Problem 20

Revision as of 21:46, 11 October 2010 by Sendhil (talk | contribs) (Added a minor point about checking the solution)

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, or (A).

This is easily checked by finding 45% of 40 = 18 and noticing an 18-22 record + a 6-2 record is a 24-24 record. So another reasonable strategy in this context is to just check each of the answer choices.

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