2013 AMC 10A Problem 9

Below is the professionally curated solution for Problem 9 of the 2013 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2013 AMC 10A solutions, or check the answer key.

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Concepts:percentage linear equation

Difficulty rating: 1020

In a recent basketball game, Shenille attempted only three-point shots and two-point shots. She was successful on $20\%$ of her three-point shots and $30\%$ of her two-point shots. Shenille attempted $30$ shots. How many points did she score?

$12$

$18$

$24$

$30$

$36$

Solution:

Let $x$ be the number of two-point shots and $y$ be the number of three-point shots.

Then, Shenille scores $.3x$ two-points shots and $.2y$ three-point shots, for a total score of $2 \cdot .3x + 3 \cdot .2y = .6x + .6y.$

We know that $x + y = 30$ $.6(x + y) = 18.$

Thus, B is the correct answer.

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