2004 AMC 12B Problem 5

Below is the professionally curated solution for Problem 5 of the 2004 AMC 12B, 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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Concepts:ratio and proportionlinear equation

Difficulty rating: 1150

5.

On a trip from the United States to Canada, Isabella took dd U.S. dollars. At the border she exchanged them all, receiving 1010 Canadian dollars for every 77 U.S. dollars. After spending 6060 Canadian dollars, she had dd Canadian dollars left. What is the sum of the digits of d?d?

55

66

77

88

99

Solution:

Exchanging gives 10d7\dfrac{10d}{7} Canadian dollars. After spending 60,60, she has 10d760=d.\dfrac{10d}{7} - 60 = d. Then 3d7=60,\dfrac{3d}{7} = 60, so d=140.d = 140. The sum of its digits is 1+4+0=5.1 + 4 + 0 = 5.

Thus, the correct answer is A.

Problem 5 in Other Years