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2004 AMC 12B Problem 5

Problem 5 of 25EasierAlgebra

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?

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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.

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Concepts: ratio and proportion · linear equation

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.