2013 AMC 12A Problem 5

Below is the professionally curated solution for Problem 5 of the 2013 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2013 AMC 12A solutions, or check the answer key.

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Concepts:mean algebraic manipulation

Difficulty rating: 1130

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

$15$

$20$

$25$

$30$

$35$

Solution:

The total spent was $105 + 125 + 175 = 405,$ so each fair share is $\tfrac13\cdot 405 = 135$ dollars.

Then $t = 135 - 105 = 30$ and $d = 135 - 125 = 10,$ so $t - d = 30 - 10 = 20.$

Thus, the correct answer is B.

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