AMC12 2006 B

AMC12 2006 B · Q3

AMC12 2006 B · Q3. It mainly tests Systems of equations, Arithmetic misc.

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?

一场橄榄球比赛在两支球队 Cougars 和 Panthers 之间进行。两队总共得了 34 分，且 Cougars 以 14 分的优势获胜。Panthers 得了多少分？

(A) 10 10

(B) 14 14

(D) 20 20

(E) 24 24

Answer

Correct choice: (A)

正确答案：（A）

Solution

If the Cougars won by a margin of 14 points, then the Panthers' score would be half of (34-14). That's 10 $\Rightarrow \boxed{\text{(A)}}$. Let the Panthers' score be $x$. The Cougars then scored $x+14$. Since the teams combined scored $34$, we get $x+x+14=34 \\ \rightarrow 2x+14=34 \\ \rightarrow 2x=20 \\ \rightarrow x = 10$, and the answer is $\boxed{\text{(A)}}$.

如果 Cougars 以 14 分的优势获胜，那么 Panthers 的得分是 $(34-14)$ 的一半，即 10 $\Rightarrow \boxed{\text{(A)}}$。设 Panthers 的得分为 $x$。则 Cougars 得分为 $x+14$。由于两队总得分为 $34$，有 $x+x+14=34 \\ \rightarrow 2x+14=34 \\ \rightarrow 2x=20 \\ \rightarrow x = 10$，答案是 $\boxed{\text{(A)}}$。

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