AMC 8 1999 Problem 12

AMC8 1999 年第 12 题

比与比例★★★☆☆

The ratio of the number of games won to the number of games lost (no ties) by the Middle School Middies is 11/4 . To the nearest whole percent, what percent of its games did the team lose?

中学 Middies 队赢的场数比输的场数（无平局）的比是 11/4。取最近的整数百分比，该队输掉的比赛占百分之多少？

A.24%
B.27%
C.36%
D.45%
E.73%

正确答案 · Correct Answer

解析 · Solution

Solution 1

The ratio means that for every 11 games won, 4 are lost, so the team has won

11x

games, lost

4x

games, and played

15x

games for some positive integer

x

. The percentage of games lost is just

\dfrac{4x}{15x}\times100=\dfrac{4}{15}\times 100=26.\overline{6}\%\approx\text{(B)27\%}

Alternate Solution

The Won/Lost ratio is

\displaystyle \frac{11}{4}

so, for some number

N

, the team won

11N

games and lost

4N

games. Thus, the team played

15N

games and the fraction of games lost is

\dfrac{4N}{15N}=\dfrac{4}{15}\approx 0.27=27\%.

-Clara Garza

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