Question

房间里一半的人离开了。剩下的人中有三分之一开始跳舞。此时有 $12$ 人没有跳舞。房间里原来有多少人？

Half the people in a room left. One third of those remaining started to dance. There were then $12$ people who were not dancing. What was the original number of people in the room?

$24$

$30$

$36$

$42$

$72$

答案：C

知识点：分数逆推法

难度评级：960

小提示：

一半人离开后，剩下的人数才是跳舞比例所作用的总数

After half leave, the number remaining is what the dancing fraction applies to

大提示：

$12$ 个没跳舞的人是剩余人数的 $\dfrac23$

The $12$ non-dancers are $\dfrac23$ of those remaining

解答：

在留下的人中， $\dfrac13$ 跳舞，所以 $\dfrac23$ 没跳舞。因此剩余人数的 $\dfrac23$ 等于 $12$ ，得剩余 $18$ 人。

这 $18$ 人是原来人数的一半，所以房间一开始有 $2 \times 18 = 36$ 人。

所以正确答案是 C。

Of those remaining, $\dfrac13$ danced, so $\dfrac23$ did not. Thus $\dfrac23$ of the remaining people equals $12,$ giving $18$ remaining.

Those $18$ are half the original group, so the room started with $2 \times 18 = 36$ people.

Thus, the correct answer is C .

1987 AMC 8 第 18 题

答案：C

难度评级：960

小提示：

大提示：

解答：

其他年份的第 18 题