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| − | ==Problem 12==
| + | #redirect [[2011 AMC 12A Problems/Problem 6]] |
| − | 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?
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| − | <math>\text{(A)}\,13 \qquad\text{(B)}\,14 \qquad\text{(C)}\,15 \qquad\text{(D)}\,16 \qquad\text{(E)}\,17</math>
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| − | == Solution ==
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| − | Suppose there were <math>x</math> three-point shots, <math>y</math> two-point shots, and <math>z</math> one-point shots. Then we get the following system of equations:
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| − | <cmath>\begin{align}
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| − | 3x=2y\\ z=y+1\\ 3x+2y+z=61
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| − | \end{align}</cmath>
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| − | The value we are looking for is <math>z</math>, which is easily found to be <math>z=\boxed{13 \ \mathbf{(A)}}</math>.
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