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 $d?$

$5$

$6$

$7$

$8$

$9$

Answer: A

Concepts:linear equation ratio and proportion

Difficulty rating: 1100

Solution:

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.

2004 AMC 10B Problem 7

Answer: A

Difficulty rating: 1100

Solution:

Problem 7 in Other Years