Question

Fitness for Families offers two exercise class options. The first option costs $50 plus $2 per class. The second option has no initial fee, but each class is $6. You want to compare the 2 options to see which option is the better choice.

Part A. Should you use equations or inequalities to model this story? Write one complete sentence explaining how you know.
Part B. Write a system of equations or inequalities to model this story.
Part C. If you plan to attend 15 exercise classes, which option is the better choice?

Answer 1

We should use inequalities to model the story. For Option 1, the total cost can be expressed as C1 = 50 + 2x. For Option 2, the total cost can be expressed as C2 = 6x. If you plan to attend 15 exercise classes, Option 1 is the better choice.

Step-by-step explanation:

Part A. In this case, we should use inequalities to model the story. The reason is that there are multiple possible values for the number of classes taken, and we want to compare which option is better in terms of cost. Using inequalities will allow us to compare the costs of the two options.

Part B. Let x represent the number of classes taken. For Option 1, the total cost can be expressed as C1 = 50 + 2x. For Option 2, the total cost can be expressed as C2 = 6x.

Part C. If you plan to attend 15 exercise classes, we can substitute x = 15 into the cost equations to compare. Option 1: C1 = 50 + 2(15) = 50 + 30 = 80. Option 2: C2 = 6(15) = 90. Therefore, Option 1 is the better choice in terms of cost.