Question

Naomi wants to take fitness classes at a nearby gym, but she needs to start by selecting a membership plan. With the first membership plan, Naomi can pay $54 per month, plus $1 for each group class she attends. With the second membership plan, she'd pay $12 per month plus $3 per class.

If Naomi 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 does that take? What is that total amount Naomi will pay per month for a membership and that many classes?

Answer 1

Naomi needs to attend 21 classes per month for both gym membership plans to cost the same. At this point, the total cost for either plan is $75 per month.

Step-by-step explanation:

To determine how many classes per month Naomi needs to attend for both membership plans to cost the same, we set up two equations representing the total cost for each membership plan and solve for the number of classes.

Let's define C as the total monthly cost and x as the number of classes Naomi attends. For the first membership plan, the cost is determined by the equation C = 54 + x. For the second membership plan, the cost is determined by the equation C = 12 + 3x.

To find the point where both plans cost the same, we set the two equations equal to each other:
54 + x = 12 + 3x

Solving for x, we subtract x from both sides:
54 = 12 + 2x

Next, we subtract 12 from both sides:
42 = 2x

Finally, we divide both sides by 2 to find x:
x = 21

Naomi needs to attend 21 classes for both plans to cost the same. The total monthly cost for either plan at this point would be:

C = 54 + (1 × 21) = $75

Therefore, Naomi will pay $75 per month for a membership and attending 21 classes.

Answer 2

54+x=12+3x
X=21 =number of classes
Total amount she will pay is $75