Difference between revisions of "2011 AMC 10A Problems/Problem 12"
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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> | <math>\text{(A)}\,13 \qquad\text{(B)}\,14 \qquad\text{(C)}\,15 \qquad\text{(D)}\,16 \qquad\text{(E)}\,17</math> | ||
| + | |||
| + | == Solution == | ||
| + | |||
| + | 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: | ||
| + | <cmath>\begin{array} | ||
| + | 3x=2y\\ z=y+1\\ 3x+2y+z=61 | ||
| + | \end{array}</cmath> | ||
| + | |||
| + | The value we are looking for is <math>z</math>, which is easily found to be <math>z=\boxed{13 \ \mathbf{(A)}}</math>. | ||
Revision as of 00:11, 16 February 2011
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?
Solution
Suppose there were 
three-point shots, 
two-point shots, and 
one-point shots. Then we get the following system of equations:
\[\begin{array}
3x=2y\\ z=y+1\\ 3x+2y+z=61
\end{array}\] (Error compiling LaTeX. Unknown error_msg)
The value we are looking for is , which is easily found to be 
.
