AMC8 2007

AMC8 2007 · Q20

AMC8 2007 · Q20. It mainly tests Systems of equations, Percent.

Before district play, the Unicorns had won 45% of their basketball games. During district play, they won six more games and lost two, to finish the season having won half their games. How many games did the Unicorns play in all?

在地区赛前，独角兽队篮球比赛胜率为 45%。地区赛中，他们赢了 6 场，输了 2 场，整个赛季胜率为一半。他们总共打了多少场比赛？

(A) 48 48

(B) 50 50

(D) 54 54

(E) 60 60

Answer

Correct choice: (A)

正确答案：（A）

Solution

(A) Because $45\%$ is the same as the simplified fraction $\frac{9}{20}$, the Unicorns won 9 games for each 20 games they played. This means that the Unicorns must have played some multiple of 20 games before district play. The table shows the possibilities that satisfy the conditions in the problem. Only when the Unicorns played 40 games before district play do they finish winning half of their games. So the Unicorns played $24+24=48$ games.

（A）因为$45\%$与最简分数$\frac{9}{20}$相同，独角兽队每打20场就赢9场。这意味着独角兽队在分区赛开始前所打的场次必须是20的某个倍数。下表给出了满足题目条件的可能情况。只有当独角兽队在分区赛前打了40场时，他们最终才会赢下全部比赛的一半。因此独角兽队一共打了$24+24=48$场比赛。

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