2013 AMC 12A Problem 5

Attempt Problem 5 of the 2013 AMC 12A below, then check your answer against the professionally curated solution 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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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

Each person’s fair share is one third of the total spent

t

and

d

measure how much Tom and Dorothy each fall short of their fair share

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,

t - d = 30 - 10 = 20.

Thus, the correct answer is B.

Problem 5 in other years