2004 AMC 12B Problem 15

Attempt Problem 15 of the 2004 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2004 AMC 12B solutions, or check the answer key.

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15.

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

Answer: B

Concepts:ages place value linear equation

Difficulty rating: 1510

Small hint:

Let Jack be

10x + y

and Bill be

10y + x

Big hint:

10x + y + 5 = 2(10y + x + 5)

simplifies to

8x = 19y + 5

Solution:

Let Jack be

10x + y

and Bill be

10y + x.

Then

10x + y + 5 = 2(10y + x + 5),

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.