AMC 8 2004 Problem 20

AMC8 2004 年第 20 题

比与比例★★★☆☆

Two-thirds of the people in a room are seated in three-fourths of the chairs. The rest of the people are standing. If there are 6 empty chairs, how many people are in the room?

房间里的人坐在的椅子上。其余的人都站着。如果有 6 张空椅子，则房间里有多少人？

A.12
B.18
C.24
D.27
E.36

正确答案 · Correct Answer

解析 · Solution

Solution 1

Working backwards, if 3/4 of the chairs are taken and 6 are empty, then there are three times as many taken chairs as empty chairs, or

3 \cdot 6 = 18

. If

x

is the number of people in the room and 2/3 are seated, then

\frac23 x = 18

and

x = (\text{D) 27}

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