2013 AMC 10A Problems/Problem 9

Problem

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?

$\textbf{(A)}\ 12 \qquad\textbf{(B)}\ 18 \qquad\textbf{(C)}\ 24 \qquad\textbf{(D)}\ 30 \qquad\textbf{(E)}\ 36$

Solution

Let the number of attempted three-point shots made be $x$ and the number of attempted two-point shots be $y$ . We know that $x+y=30$ , and we need to evaluate $(0.2\cdot3)x +(0.3\cdot2)y$ , as we know that the

three-point shots are worth 3 points and that she made 20% of them and that the two-point shots are worth 2 and that she made 30% of them.

Simplifying, we see that this is equal to $0.6x + 0.6y = 0.6(x+y)$ . Plugging in $x+y=30$ , we get $0.6(30) = 18$ , $\textbf{(B)}$ .

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2013 AMC 10A Problems/Problem 9

Problem

Solution