2013 AMC 12A Problem 6

Attempt Problem 6 of the 2013 AMC 12A below, then check your answer against the professionally curated solution 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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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

Let

x

be the number of three-point attempts, so

30 - x

are two-point attempts

Her score is

0.2\cdot 3\cdot x + 0.3\cdot 2\cdot(30 - x);

the

x

terms cancel

If Shenille attempted

x

three-point shots and

30 - x

two-point shots, she scored

\begin{gathered} 0.2\cdot 3\cdot x + 0.3\cdot 2\cdot(30 - x) \\ = 0.6x + 0.6(30 - x) \\ = 0.6\cdot 30 = 18 \end{gathered}

points.

Thus, the correct answer is B.

Problem 6 in other years