2006 AMC 12B Problems/Problem 3: Difference between revisions

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
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 12 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing

@@ 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===

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