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2013 AMC 12A Problem 5

Problem 5 of 25EasierAlgebra

Tom, Dorothy, and Sammy went on a vacation and agreed to split the costs evenly. During their trip Tom paid $105,\$105, Dorothy paid $125,\$125, and Sammy paid $175.\$175. In order to share the costs equally, Tom gave Sammy tt dollars, and Dorothy gave Sammy dd dollars. What is td?t - d?

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Solution

The total spent was 105+125+175=405,105 + 125 + 175 = 405, so each fair share is 13405=135\tfrac13\cdot 405 = 135 dollars. Then t=135105=30t = 135 - 105 = 30 and d=135125=10,d = 135 - 125 = 10, so td=3010=20.t - d = 30 - 10 = 20. Thus, the correct answer is B.

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Concepts: mean · algebraic manipulation

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