A gym charges its customers an initial membership fee, plus an hourly fee. The graph shows the cost of using the gym.

Question

A gym charges its customers an initial membership fee, plus an hourly fee. The graph shows the cost of using the gym.

Part A: What is the initial fee charged to customers for using the gym? What is the hourly rate? Explain your reasoning.

Part B: Lina has the option of purchasing an unlimited weekly pass at the gym for $100. She normally uses the gym 3 times per week, no more than 2 hours each time. Is it cheaper for Lina to purchase the unlimited weekly pass? Why or why not? Explain your reasoning.

Answer 1

The initial fee per the graph is $20 (the y-intercept, with no gym time). Her cost per hr is the slope (rise/run). From the graph that's (50 - 20)/(6 - 0) using two convenient points, or 30/6 = $5/hr.

So the linear eqn is C = 5h + 20, where h = no. hrs, C = total cost.

If she uses the gym 3 times/wk x 2 hrs/time max., that's 6 hrs/wk. C = 5(6) + 20 = $50 (also visible on the graph).

The unltd weekly pass for $100/wk would cost more, so that is not a good option based on projected usage.

Can you use the eqn to figure out h.m. hours/wk she would need to use the gym to make the weekly pass worth it?