2011 AMC 10A Problem 12

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?

13

14

15

16

17

Answer: A

Concepts:linear equation

Difficulty rating: 960

Small hint:

Let

x

be the number of two-point shots

Big hint:

The points from two-point shots equal the points from three-point shots

Solution:

Let

x

be the number of successful two-point shots. Then we have that

2x + 2x + (x + 1) = 61,

which simplifies to

5x + 1 = 61

x = 12.

The number of successful free throws is then

12 + 1 = 13.

Thus, A is the correct answer.