AMC 8 1995 Problem 14

AMC8 1995 年第 14 题

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A team won 40 of its first 50 games. How many of the remaining 40 games must this team win so it will have won exactly 70 % of its games for the season?

一支队伍在前 50 场比赛中赢了 40 场。在剩下的 40 场比赛中他们必须赢多少场，才能使整个赛季的胜率恰好为 70%？

A.20
B.23
C.28
D.30
E.35

正确答案 · Correct Answer

解析 · Solution

Solution 1

Noting that 70% is the same as

\displaystyle \frac{70}{100}

\displaystyle \frac{7}{10}

, and that, when x is the amount of wins in the last 40 games, the fraction of games won is

\displaystyle \frac{40+x}{50+40}

\displaystyle \frac{40+x}{90}

, all we have to do is set them equal:

\displaystyle \frac{40+x}{90}=\frac{7}{10}

40+x=63

x=\text{(B)23}

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