Question

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.

a. 4x + 2y = 96; x + y = 72
b. 2x + 4y = 96; x + y = 72
c. 4x + 2y = 72; x + y = 96
d. 2x + 4y = 72; x + y = 96

Answer 1

The correct system of equations is a. 4x + 2y = 96; x + y = 72. x represents the number of pool passes and y represents the number of gym memberships.

Step-by-step explanation:

The correct system of equations that represents the relationships between pool passes, gym memberships, and the costs is a. 4x + 2y = 96 and x + y = 72.

Where:

• x represents the number of pool passes
• y represents the number of gym memberships

To find the system of equations, we need to consider two things:

1. The cost of the pool passes, which is represented by the equation 4x + 2y = 96. This equation takes into account that each pool pass costs 4 units and each gym membership costs 2 units.
2. The total number of passes and memberships, which is represented by the equation x + y = 72. This equation states that the sum of pool passes and gym memberships is 72.