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2004 AMC 10B Problem 7

Problem 7 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

Isabella received 107d\dfrac{10}{7}d Canadian dollars and spent 60,60, leaving d.d. So 107d60=d. \dfrac{10}{7}d - 60 = d. Then 37d=60,\dfrac{3}{7}d = 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: linear equation · ratio and proportion

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