2011 AMC 10A Problem 12

Below is the professionally curated solution for Problem 12 of the 2011 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2011 AMC 10A solutions, or check the answer key.

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Concepts:linear equation

Difficulty rating: 960

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?

$13$

$14$

$15$

$16$

$17$

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.

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