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 $A \lt B.$ How many dollars must LeRoy give to Bernardo so that they share the costs equally?

$\dfrac{A+B}{2}$

$\dfrac{A-B}{2}$

$\dfrac{B-A}{2}$

$B-A$

$A+B$

Solution:

The total cost is $A+B,$ so each person's fair share is $\dfrac{A+B}{2}.$

LeRoy paid $A,$ which is less than his share, so he must give Bernardo $\dfrac{A+B}{2}-A=\dfrac{B-A}{2}.$

Thus, the correct answer is C.

2011 AMC 12B Problem 3

Solution:

Problem 3 in Other Years