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. $\newline$ )) 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? $\newline$ If Naomi attends $\square$ classes per month, she will pay $\$$ for either membership plan.

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Q. 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.

\newline

)) 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?

\newline

If Naomi attends

\square

classes per month, she will pay

\$

for either membership plan.

Identify Membership Plans: Let's call the number of classes Naomi attends ＂ $x$ ＂. For the first membership plan, the cost is $\$54$ plus $\$1$ per class. So the total cost for the first plan is $54 + x$ dollars.
Calculate Total Costs: For the second membership plan, the cost is $\$12$ plus $\$3$ per class. So the total cost for the second plan is $12 + 3x$ dollars.
Set Equations Equal: We want to find out when the costs are the same, so we set the two expressions equal to each other: $54 + x = 12 + 3x$ .
Solve for x: Now, we solve for x. Subtract $x$ from both sides to get $54 = 12 + 2x$ .