2011 AMC 10A Problems/Problem 12
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 two-point 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?
Suppose there were three-point shots, two-point shots, and one-point shots. Then we get the following system of equations:
The value we are looking for is , which is easily found to be .