2004 AMC 8 第 20 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
20.
一个房间里三分之二的人坐在四分之三的椅子上。剩下的人站着。如果有 把空椅子，房间里有多少人？
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 empty chairs, how many people are in the room?
小提示：
空椅子是所有椅子的剩余四分之一
The empty chairs are the remaining one-fourth of the chairs.
大提示：
坐着的人是所有人的三分之二
The seated people are two-thirds of all the people.
解答：
因为 的椅子被坐了，所以 把空椅子是所有椅子的 。因此共有 把椅子。
坐着的人数是 乘 ，即 。
这 个坐着的人是所有人的 ，所以总人数为 。
所以正确答案是 D。
Since of the chairs are occupied, the empty chairs are of all the chairs. Thus there are chairs.
The number of seated people is of which is
Those seated people are of all the people, so the total number of people is
Thus, D is the correct answer.
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