2014 AMC 12A Problem 2

Problem 2 of 25EasierAlgebra

At the theater children get in for half price. The price for

5

adult tickets and

4

child tickets is

\$24.50.

How much would

8

adult tickets and

6

child tickets cost?

Show solution

Solution

Since a child ticket is half an adult ticket,

5

adult and

4

child tickets equal

5+\tfrac12\cdot4=7

adult tickets, so one adult ticket costs

\dfrac{24.50}{7}=\$3.50.

The second purchase equals

8+\tfrac12\cdot6=11

adult tickets, costing

11\cdot 3.50=\$38.50.

Thus, the correct answer is B.