2011 AMC 10B Problem 4

Question

LeRoy and Bernardo went on a week-long trip together and agreed to share the costs equally. Over the week, each of them paid for various joint expenses such as gasoline and car rental. At the end of the trip it turned out that LeRoy had paid

A

dollars and Bernardo had paid

B

dollars, where

A < B.

How many dollars must LeRoy give to Bernardo so that they share the costs equally?

\dfrac{A + B}{2}

\dfrac{A - B}{2}

\dfrac{B - A}{2}

B - A

A + B

Answer: C

Concepts:algebraic manipulation mean

Difficulty rating: 870

Small hint:

Compare how much more Bernardo paid than LeRoy

Big hint:

Only half of the difference has to be transferred

Solution:

The amount they each would have to pay is

\dfrac{A+B}2,

and LeRoy paid

A.

Thus, he has to pay

\dfrac{A+B}2-A = \dfrac{B-A}2

more.

Thus, the correct answer is C .