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?

$10$

$15$

$20$

$25$

$30$

Solution:

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

Then, the number of made three-point shots is $0.4 t,$ implying that the number of points made off of three-point shots is $1.2t.$

Similarly, the number of two-point shots is $1.5t,$ so the number of made two-point shots is $0.75t,$ suggesting that the number of points made off of 2 point shots is $1.5t.$

This makes the total number of points scored equal to: $2.7t=54,$ and so, $t=20.$

Thus, the correct answer is C .

2013 AMC 10B Problem 10

Solution:

Problem 10 in Other Years