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?

99

1818

2727

3636

4545

Answer: B
Concepts:agesplace valuelinear equation
Difficulty rating: 1510
Solution:

Let Jack be 10x+y10x + y and Bill be 10y+x.10y + x. Then 10x+y+5=2(10y+x+5),10x + y + 5 = 2(10y + x + 5), so 8x=19y+5.8x = 19y + 5. Testing digits, only y=1,x=3y = 1, x = 3 works, so Jack is 3131 and Bill is 13.13. The difference is 3113=18.31 - 13 = 18.

Thus, the correct answer is B.

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