2006 AMC 12B Problem 3

Problem 3 of 25EasierAlgebra

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?

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Solution

Let

c

and

p

be the Cougars’ and Panthers’ scores. Then

c + p = 34

and

c - p = 14.

Subtracting gives

2p = 20,

p = 10.

Thus, the correct answer is A.

Concepts: system of equations

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.