2007 AMC 8 Problem 20
Attempt Problem 20 of the 2007 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
20.
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?
Answer: A
Small hint:
Let be the number of games before district play.
Big hint:
Write an equation comparing total wins after district play with half of all games played.
Solution:
Let be the number of games the Unicorns had played before district play. Then they had won games before district play and games after district play.
In total, they played games. The problem statement tells us that
Solving gives , so , and . Therefore, the Unicorns played games in all.
Thus, A is the correct answer.
Problem 20 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
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