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:system of equations substitution

Difficulty rating: 1170

Solution:

Let $a$ be the number of two-point shots. The two-point shots score $2a$ points, and the three-point shots score the same $2a$ points. The free throws number $a + 1$ and score $a + 1$ points.

The total is $\begin{aligned} 2a + 2a + (a + 1) \\ = 5a + 1 = 61, \end{aligned}$ so $a = 12$ and the free throws number $a + 1 = 13.$

Thus, the correct answer is A.

2011 AMC 12A Problem 6

Answer: A

Difficulty rating: 1170

Solution:

Problem 6 in Other Years