2006 AMC 10B 第 3 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

3.

Cougars 和 Panthers 两队进行了一场橄榄球比赛。两队总共得 3434 分,Cougars 以 1414 分优势获胜。Panthers 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 3434 points, and the Cougars won by a margin of 1414 points. How many points did the Panthers score?

1010

1414

1717

2020

2424

答案:A
知识点:方程组一次方程
难度评级:830
解答:

ccpp 分别为 Cougars 和 Panthers 的得分。则 c+p=34c+p=34,且 cp=14c-p=14。两式相减得 2p=202p=20,所以 p=10p=10

所以正确答案是 A

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

Thus, the correct answer is A.

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