AMC12 2020 B

AMC12 2020 B · Q5

AMC12 2020 B · Q5. It mainly tests Linear equations, Fractions.

Teams A and B are playing in a basketball league where each game results in a win for one team and a loss for the other team. Team A has won $\frac{2}{3}$ of its games and team B has won $\frac{5}{8}$ of its games. Also, team B has won 7 more games and lost 7 more games than team A. How many games has team A played?

A队和B队参加篮球联赛，每场比赛一方胜一方负。A队赢了其比赛的 $\frac{2}{3}$，B队赢了其比赛的 $\frac{5}{8}$。此外，B队比A队多赢7场，也多输7场。A队总共打了多少场比赛？

(A) 21 21

(B) 27 27

(D) 48 48

(E) 63 63

Answer

Correct choice: (C)

正确答案：（C）

Solution

Let $g$ be the number of games played by A; then B played $g + 7 + 7$ games. Focusing on the number of games won by B implies $\frac{2}{3}g + 7 = \frac{5}{8}(g + 14)$. Solving this equation gives $g = 42$.

设A队打了$g$场比赛，则B队打了$g + 7 + 7$场比赛。关注B队赢得的场次，得到 $\frac{2}{3}g + 7 = \frac{5}{8}(g + 14)$。解此方程得 $g = 42$。

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