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

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.

2011 AMC 10A Problem 12

Answer: A

Difficulty rating: 960

Solution:

Problem 12 in Other Years