Question

一家公司经理原计划从公司基金中给每位员工发 $\$50$ 奖金，但基金比所需金额少 $\$5$ 。于是经理改为给每位员工发 $\$45$ 奖金，并在公司基金中留下 $\$95$ 。发放任何奖金之前，公司基金中有多少钱？

The manager of a company planned to distribute a $\$50$ bonus to each employee from the company fund, but the fund contained $\$5$ less than what was needed. Instead the manager gave each employee a $\$45$ bonus and kept the remaining $\$95$ in the company fund. The amount of money in the company fund before any bonuses were paid was

$\$945$

$\$950$

$\$955$

$\$990$

$\$995$

答案：E

知识点：一次方程

难度评级：1090

小提示：

设员工人数为 $n$ ；基金数等于 $50n - 5$ ，也等于 $45n + 95$ 。

Let $n$ be the number of employees; the fund equals $50n - 5$ and also $45n + 95$

大提示：

令两个基金表达式相等，解出 $n$ ，再计算基金数。

Set the two expressions for the fund equal to solve for $n,$ then compute the fund

解答：

设员工人数为 $n$ 。基金数为 $50n - 5$ （比每人 $50$ 美元少五美元），也等于 $45n + 95$ 。

令 $50n - 5 = 45n + 95$ ，得 $5n = 100$ ，所以 $n = 20$ 。基金数为 $45 \cdot 20 + 95 = 995$ 美元。

所以正确答案是 E。

Let $n$ be the number of employees. The fund is $50n - 5$ (five dollars short of $50$ each) and also $45n + 95.$

Setting $50n - 5 = 45n + 95$ gives $5n = 100,$ so $n = 20.$ The fund is $45 \cdot 20 + 95 = 995.$

Thus, the correct answer is E .

1996 AMC 8 第 23 题

答案：E

难度评级：1090

小提示：

大提示：

解答：

其他年份的第 23 题