Question

Terrell wants to take group fitness classes at a nearby gym, but needs to start by selecting a membership plan. With the first membership plan, Terrell can pay $30 per month, plus $1 for each group class he attends. Alternately, he can get the second membership plan and pay $15 per month plus $4 per class. If Terrell attends a certain number of classes in a month, the two membership plans end up costing the same total amount. How many classes per month is that? What is that total amount?

Answer 1

Let's assume that Terrell attends x number of classes in a month. Then, the total cost of the first membership plan would be:

Cost of the first membership plan = $30 + $1 * x

Similarly, the total cost of the second membership plan would be:

Cost of the second membership plan = $15 + $4 * x

As per the problem statement, both membership plans cost the same when Terrell attends a certain number of classes in a month. So, we can equate the above two expressions and solve for x:

$30 + $1 * x = $15 + $4 * x

$2 * x = $15

x = 7.5

Since the number of classes cannot be a fraction, we can round up to the nearest integer, which is 8. Therefore, Terrell needs to attend 8 classes per month to make both membership plans cost the same.

To find the total amount, we can substitute x = 8 in either of the above expressions:

Total amount = $30 + $1 * 8 = $38

Therefore, Terrell needs to attend 8 classes per month, and the total amount would be $38.