smc

Question

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?

Accepted Answer

For the points made from two-point shots and from three-point shots to be equal, the numbers of made shots are in a 3:2 ratio. Therefore, assume they made 3x and 2x two- and three- point shots, respectively, and thus 3x+1 free throws. The total number of points is 2 (3x) + 3 (2x) + 1 (3x+1) = 15x+1 Set that equal to 61, we get x = 4, and therefore the number of free throws they made 3 4 + 1 = 13 13