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2013 AMC 10A Problem 5

Problem 5 of 25EasierProbability & StatisticsArithmetic

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 t−d?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 t−d=30−10=20t-d=30-10=20. Thus, B is the correct answer.
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