2004 AMC 10B Problem 7

Question

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{10}{7}d

Canadian dollars

Set

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

and solve for

d

Isabella received

\dfrac{10}{7}d

Canadian dollars and spent

60,

leaving

d.

So

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

Then

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

so

d = 140.

The sum of its digits is

1 + 4 + 0 = 5.

Thus, the correct answer is A.

Problem 7 in other years