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2013 AMC 10A 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 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 cost was $105+$125+$175=$405\$105+\$125+\$175=\$405, so each person’s share was $405÷3=$135\$405\div3=\$135. Tom paid $30\$30 less than his share, and Dorothy paid $10\$10 less than her share, so t=30t=30 and d=10d=10. Therefore td=3010=20t-d=30-10=20. Thus, B is the correct answer.

More practice

Concepts: mean · money

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