Question

在奥林匹克高中， $\tfrac25$ 的高一学生和 $\tfrac45$ 的高二学生参加了 AMC $10$ 。已知参加考试的高一学生人数和高二学生人数相同。下列哪一项一定成立？

At Olympic High School, $\tfrac25$ of the freshmen and $\tfrac45$ of the sophomores took the AMC $10.$ Given that the number of freshmen and sophomore contestants was the same, which of the following must be true?

高二学生人数是高一学生人数的五倍。

There are five times as many sophomores as freshmen.

高二学生人数是高一学生人数的两倍。

There are twice as many sophomores as freshmen.

高一学生人数和高二学生人数相同。

There are as many freshmen as sophomores.

高一学生人数是高二学生人数的两倍。

There are twice as many freshmen as sophomores.

高一学生人数是高二学生人数的五倍。

There are five times as many freshmen as sophomores.

答案：D

知识点：比与比例一次方程

难度评级：1020

小提示：

设高一和高二学生总人数分别为 $f$ 和 $s$ ，并令参加考试的人数相等。

Let $f$ and $s$ be the numbers of freshmen and sophomores, and set the two contestant counts equal

大提示：

解方程 $\tfrac25 f = \tfrac45 s$ ，把 $f$ 用 $s$ 表示。

Solve $\tfrac25 f = \tfrac45 s$ for $f$ in terms of $s$

解答：

设高一和高二学生总人数分别为 $f$ 和 $s$ 。参加考试的人数相同，所以 $\tfrac25 f = \tfrac45 s\text{。}$

两边乘以 $5$ ，得 $2f = 4s$ ，所以 $f = 2s$ 。高一学生人数是高二学生人数的两倍。

所以正确答案是 D。

Let $f$ and $s$ be the numbers of freshmen and sophomores. The contestant counts are equal, so $\tfrac25 f = \tfrac45 s.$

Multiplying by $5$ gives $2f = 4s,$ so $f = 2s.$ There are twice as many freshmen as sophomores.

Thus, the correct answer is D.

2000 AMC 10 第 8 题

答案：D

难度评级：1020

小提示：

大提示：

解答：

其他年份的第 8 题