2006 AMC 12B 第 3 题

Question

Cougars 队和 Panthers 队进行了一场橄榄球比赛。两队总共得了

34

分，Cougars 队以

14

分的优势获胜。Panthers 队得了多少分？

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

知识点：方程组

设两队得分为

c

和

p

，则

c + p = 34

，且

c - p = 14

。

Let

c

and

p

be the two scores, with

c + p = 34

and

c - p = 14

两个方程相减可得到

2p

Subtracting the two equations isolates

2p

设 Cougars 和 Panthers 的得分分别为

c

和

p

，则

c + p = 34

，且

c - p = 14

。

相减得

2p = 20

，所以

p = 10

。

因此，正确答案是 A。

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.

其他年份的第 3 题