Difference between revisions of "2011 AMC 10A Problems/Problem 12"
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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>. | 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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| + | == See Also == | ||
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| + | {{AMC10 box|year=2011|ab=A|num-b=11|num-a=13}} | ||
Revision as of 10:50, 8 May 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 
.
See Also
| 2011 AMC 10A (Problems • Answer Key • Resources) | ||
| 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 | ||
