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

(Redirected page to 2011 AMC 12A Problems/Problem 6)
(Tag: New redirect)
 
Line 1: Line 1:
==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?
 
 
 
<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{align}
 
3x=2y\\ z=y+1\\ 3x+2y+z=61
 
\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>.
 
 
 
 
 
== See Also ==
 
 
 
{{AMC10 box|year=2011|ab=A|num-b=11|num-a=13}}
 
{{MAA Notice}}
 

Latest revision as of 19:06, 27 June 2020

Invalid username
Login to AoPS