Difference between revisions of "2006 AMC 12B Problems/Problem 3"

Latest revision as of 12:39, 13 February 2016

Problem

A football game was played between two teams, the Cougars and the Panthers. The two teams scored a total of 34 points, and the Cougars won by a margin of 14 points. How many points did the Panthers score?

$\text {(A) } 10 \qquad \text {(B) } 14 \qquad \text {(C) } 17 \qquad \text {(D) } 20 \qquad \text {(E) } 24$

Solution

Solution 1

If the Cougars won by a margin of 14 points, then the Panthers' score would be half of (34-14). That's 10 $\Rightarrow \boxed{\text{(A)}}$ .

Solution 2

Let the Panthers' score be $x$ . The Cougars then scored $x+14$ . Since the teams combined scored $34$ , we get $x+x+14=34 \\ \rightarrow 2x+14=34 \\ \rightarrow 2x=20 \\ \rightarrow x = 10$ ,

and the answer is $\boxed{\text{(A)}}$ .

2006 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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All AMC 12 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

@@ Line 9: / Line 9: @@
 ===Solution 1===
-If the Cougars won by a margin of 14 points, then the Panthers' score would be half of (34-14). That's 10 <math>\Rightarrow \text{(A)}</math>.
+If the Cougars won by a margin of 14 points, then the Panthers' score would be half of (34-14). That's 10 <math>\Rightarrow \boxed{\text{(A)}}</math>.
 ===Solution 2===
 Let the Panthers' score be <math>x</math>. The Cougars then scored <math>x+14</math>. Since the teams combined scored <math>34</math>, we get <math>x+x+14=34 \\ \rightarrow 2x+14=34 \\ \rightarrow 2x=20 \\ \rightarrow x = 10</math>,
 and the answer is  <math>\boxed{\text{(A)}}</math>.

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