2006 AMC 10B Problem 3

Attempt Problem 3 of the 2006 AMC 10B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2006 AMC 10B solutions, or check the answer key.

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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?

$10$

$14$

$17$

$20$

$24$

Answer: A

Concepts:system of equations linear equation

Difficulty rating: 830

Solution:

Let $c$ and $p$ be the Cougars' and Panthers' scores. Then $c+p=34$ and $c-p=14.$ Subtracting gives $2p=20,$ so $p=10.$

Thus, the correct answer is A.

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