A.2.17.2 What's the Deal?

A recreation center is offering special prices on its pool passes and gym memberships for the summer. On the first day of the offering, a family paid $96 for 4 pool passes and 2 gym memberships. Later that day, an individual bought a pool pass for herself, a pool pass for a friend, and 1 gym membership. She paid $72.  Write a system of equations that represents the relationships between pool passes, gym memberships, and the costs. Be sure to state what each variable represents.

Find the price of a pool pass and the price of a gym membership by solving the system algebraically.

Graph the equations in the system. Make 1-2 observations about your graphs.

Here are some ways to think about the situation:       The family purchased twice the number of pool passes and gym memberships as the individual did, but they did not pay twice as much, so the prices of passes and memberships must have been different for the two purchases. The person who bought half as many passes and memberships did not pay half as much, which meant that different prices applied to the two transactions. The special rates for a family of 4 did not apply to individuals, hence the different prices.