2013 AMC 10A Problem 5

Question

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 costs equally, Tom gave Sammy

t

dollars, and Dorothy gave Sammy

d

dollars. What is

t-d?

15

20

25

30

35

Concepts:mean money

First find the total trip cost and each person’s fair share

Tom and Dorothy each pay Sammy the amount they are short of a fair share

The total cost was

\$105+\$125+\$175=\$405

, so each person’s share was

\$405\div3=\$135

.

Tom paid

\$30

less than his share, and Dorothy paid

\$10

less than her share, so

t=30

and

d=10

.

Therefore

t-d=30-10=20

.

Thus, B is the correct answer.

Problem 5 in other years