Question

在参加学校派对的学生中， $60\%$ 是女生， $40\%$ 喜欢跳舞。后来又来了 $20$ 名男生，他们都喜欢跳舞，此时派对上的学生中女生占 $58\%$ 。现在派对上有多少名学生喜欢跳舞？

Of the students attending a school party, $60\%$ of the students are girls, and $40\%$ of the students like to dance. After these students are joined by $20$ more boy students, all of whom like to dance, the party is now $58\%$ girls. How many students now at the party like to dance?

答案

答案：252

知识点：百分数一次方程

难度评级：1750

解答：

设原来派对上有 $x$ 名学生，则女生有 $0.6x$ 人，喜欢跳舞的有 $0.4x$ 人。 $20$ 名男生到来后，女生人数不变，总人数变为 $x + 20$ ，所以 $0.6x = 0.58(x + 20)$ 。于是 $0.02x = 11.6$ ，得 $x = 580$ 。

现在喜欢跳舞的学生人数为 $0.4 \cdot 580 + 20 = 232 + 20 = 252$ 。

Let $x$ be the number of students originally at the party, so $0.6x$ are girls and $0.4x$ like to dance. When the $20$ boys arrive, the number of girls is unchanged but the total becomes $x + 20,$ so $0.6x = 0.58(x + 20).$ Then $0.02x = 11.6,$ giving $x = 580.$

The number of students who now like to dance is $0.4 \cdot 580 + 20 = 232 + 20 = 252.$

2008 AIME I 第 1 题

答案：252

难度评级：1750

解答：

其他年份的第 1 题