Difference between revisions of "2011 AMC 10A Problems/Problem 12"

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Revision as of 12:00, 4 July 2013

Problem 12

The players on a basketball team made some three-point shots, some two-point shots, and some one-point free throws. They scored as many points with two-point shots as with three-point shots. Their number of successful free throws was one more than their number of successful two-point shots. The team's total score was 61 points. How many free throws did they make?

$\text{(A)}\,13 \qquad\text{(B)}\,14 \qquad\text{(C)}\,15 \qquad\text{(D)}\,16 \qquad\text{(E)}\,17$

Solution

Suppose there were $x$ three-point shots, $y$ two-point shots, and $z$ one-point shots. Then we get the following system of equations: \begin{align} 3x=2y\\ z=y+1\\ 3x+2y+z=61 \end{align}

The value we are looking for is $z$, which is easily found to be $z=\boxed{13 \ \mathbf{(A)}}$.


See Also

2011 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 11
Followed by
Problem 13
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions

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