2004 AMC 12B Problem 5

Attempt Problem 5 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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

On a trip from the United States to Canada, Isabella took

d

U.S. dollars. At the border she exchanged them all, receiving

10

Canadian dollars for every

7

U.S. dollars. After spending

60

Canadian dollars, she had

d

Canadian dollars left. What is the sum of the digits of

d?

5

6

7

8

9

Exchanging

d

U.S. dollars gives

\dfrac{10d}{7}

Canadian dollars

Set

\dfrac{10d}{7} - 60 = d

and solve for

d

Exchanging gives

\dfrac{10d}{7}

Canadian dollars. After spending

60,

she has

\dfrac{10d}{7} - 60 = d.

Then

\dfrac{3d}{7} = 60,

d = 140.

The sum of its digits is

1 + 4 + 0 = 5.

Thus, the correct answer is A.

Problem 5 in other years