2011 AMC 10A Problems/Problem 12: Difference between revisions
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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: | 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{ | <cmath>\begin{align} | ||
3x=2y\\ z=y+1\\ 3x+2y+z=61 | 3x=2y\\ z=y+1\\ 3x+2y+z=61 | ||
\end{ | \end{align}</cmath> | ||
The value we are looking for is <math>z</math>, which is easily found to be <math>z=\boxed{13 \ \mathbf{(A)}}</math>. | 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 23:13, 15 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:
The value we are looking for is , which is easily found to be 
.
