Difference between revisions of "2006 AMC 12B Problems/Problem 3"
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== Problem == | == 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? | ||
| + | |||
| + | <math> | ||
| + | \text {(A) } 10 \qquad \text {(B) } 14 \qquad \text {(C) } 17 \qquad \text {(D) } 20 \qquad \text {(E) } 24 | ||
| + | </math> | ||
== Solution == | == 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 <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>. | ||
== See also == | == See also == | ||
| − | + | {{AMC12 box|year=2006|ab=B|num-b=2|num-a=4}} | |
| + | {{MAA Notice}} | ||
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?
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 
.
Solution 2
Let the Panthers' score be 
. The Cougars then scored 
. Since the teams combined scored 
, we get 
,
and the answer is 
.
See also
| 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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
