Problem:
Before district play, the Unicorns had won of their basketball games. During district play, they won six more games and lost two, to finish the season having won half their games. How many games did the Unicorns play in all?
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Answer Choices:
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Solution:
Because is the same as the simplified fraction , the Unicorns won games for each games they played. This means that the Unicorns must have played some multiple of games before district play. The table shows the possibilities that satisfy the conditions in the problem.
Only when the Unicorns played games before district play do they finish winning half of their games. So the Unicorns played games.
Let be the number of Unicorn games before district play. Then . Solving for yields
So the total number of games is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions