1964 AMC 12 第 23 题

Question

两个数的差、和与积之比为

1:7:24

。这两个数的乘积是：

Two numbers are such that their difference, their sum, and their product are to one another as

1:7:24.

The product of the two numbers is:

6

12

24

48

96

将差、和、积分别表示为

k

、

7k

、

24k

Represent the difference, sum, and product by

k,

7k,

and

24k

两个数分别为

\frac{7k+k}{2}

和

\frac{7k-k}{2}

The two numbers are

\frac{7k+k}{2}

and

\frac{7k-k}{2}

设差为

k

，和为

7k

。两个数为

4k

和

3k

，所以乘积为

12k^2

。而比值还说明乘积为

24k

。由于两数不同，

k\ne0

，故

k=2

，乘积为

48

。

因此，正确答案是 D。

Let the difference be

k

and the sum be

7k.

The numbers are

4k

and

3k,

so their product is

12k^2.

But the ratio also says the product is

24k.

For distinct numbers

k\ne0,

so

k=2

and the product is

48.

Therefore, the correct answer is D.

其他年份的第 23 题