Problem:
The players on a basketball team made some three-point shots, some two-point shots, and some one-point free throws. They scored as many points with twopoint shots as with three-point shots. Their number of successful free throws was one more than their number of successful two-point shots. The team's total score was 61 points. How many free throws did they make?
Answer Choices:
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Solution:
Let , and be the number of successful three-point shots, two-point shots, and free throws, respectively. Then the given conditions imply
Solving results in , and . Hence the team made 13 free throws.
The problems on this page are the property of the MAA's American Mathematics Competitions