Question

Jack 年龄的两个数字与 Bill 年龄的两个数字相同，但顺序相反。五年后，Jack 的年龄将是 Bill 那时年龄的两倍。他们现在年龄的差是多少？

The two digits in Jack's age are the same as the digits in Bill's age, but in reverse order. In five years Jack will be twice as old as Bill will be then. What is the difference in their current ages?

$9$

$18$

$27$

$36$

$45$

答案：B

知识点：年龄问题位值一次方程

难度评级：1510

解答：

设 Jack 为 $10x + y$ ，Bill 为 $10y + x$ ，则 $10x + y + 5 = 2(10y + x + 5)$ ，所以 $8x = 19y + 5$ 。检验数字，只有 $y = 1, x = 3$ 可行，因此 Jack 是 $31$ 岁，Bill 是 $13$ 岁。差为 $31 - 13 = 18$ 。

因此正确答案是 B。

Let Jack be $10x + y$ and Bill be $10y + x.$ Then $10x + y + 5 = 2(10y + x + 5),$ so $8x = 19y + 5.$ Testing digits, only $y = 1, x = 3$ works, so Jack is $31$ and Bill is $13.$ The difference is $31 - 13 = 18.$

Thus, the correct answer is B.

2004 AMC 12B 第 15 题

答案：B

难度评级：1510

解答：

其他年份的第 15 题