Beginning and End of a Season

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During a certain season, a team won 80 percent of its first 80 games and 56 percent of its remaining games. If the team won of its games in the entire season, what was the total number of games that the team played?

Review: Beginning and End of a Season


Explanation

This question is a good candidate for plugging in answer choices, but we can set up the equation first. Let's calculate the number of wins overall:



Where R is the number of games remaining after the first 80. We are actually looking for . We can use the balance concept of averages here. The R games really pulled down the winning average, from 0.80 to approximately 0.67. Since that distance is about 0.13, and since the distance from 0.67 to 0.56 is 0.11, R must be greater than 80, probably about the size of 80. That rules out (C) through (E) and makes (A) appear probable. Let's try it. If , then





This statement is true. The correct answer is (A).


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