2013 AMC 12A Problem 6

Below is the professionally curated solution for Problem 6 of the 2013 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2013 AMC 12A solutions, or check the answer key.

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Concepts:percentage invariant

Difficulty rating: 1250

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:

If Shenille attempted $x$ three-point shots and $30 - x$ two-point shots, she scored $0.2\cdot 3\cdot x + 0.3\cdot 2\cdot(30 - x) = 0.6x + 0.6(30 - x) = 0.6\cdot 30 = 18$ points.

Thus, the correct answer is B.

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