Question

A basketball team’s players were successful on $50\%$ of their two-point shots and $40\%$ of their three-point shots, which resulted in $54$ points. They attempted $50\%$ more two-point shots than three-point shots. How many three-point shots did they attempt?

$10$

$15$

$20$

$25$

$30$

Answer: C

Concepts:percentage linear equation

Difficulty rating: 1280

Small Hint:

Let $x$ be the number of three-point attempts

Big Hint:

Translate made-shot percentages into total points in terms of $x$

Solution:

Let $t$ be the number of three-point attempts.

The number of made three-point shots is $0.4 t,$ giving $1.2t$ points.

The number of two-point attempts is $1.5t,$ so the number made is $0.75t,$ giving $1.5t$ points.

Thus the total number of points satisfies $2.7t=54,$ so $t=20.$

Thus, the correct answer is C.

2013 AMC 10B Problem 10

Answer: C

Difficulty rating: 1280

Small Hint:

Big Hint:

Solution:

Problem 10 in Other Years