Difference between revisions of "2007 AMC 8 Problems/Problem 20"
(Messy solution but it's a start) |
m (Added a minor point about checking the solution) |
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so regular season games = 40. | so regular season games = 40. | ||
| − | So the total number of games is 40 + 6 + 2 = 48. | + | So the total number of games is 40 + 6 + 2 = 48, or (A). |
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| + | 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. | ||
Revision as of 21:46, 11 October 2010
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.
