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

(Solution 2)
(Solution 2)
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===Solution 2===
 
===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 \\$,  
+
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)}}$.
+
 
 +
and the answer is  <math>\boxed{\text{(A)}}</math>.
  
 
== See also ==
 
== See also ==
 
{{AMC12 box|year=2006|ab=B|num-b=2|num-a=4}}
 
{{AMC12 box|year=2006|ab=B|num-b=2|num-a=4}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 17:08, 1 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 $\Rightarrow \text{(A)}$.

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 $\boxed{\text{(A)}}$.

See also

2006 AMC 12B (ProblemsAnswer KeyResources)
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

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