Gym A charges a registration fee of $74 plus $33 per month for members. Gym B charges a registration fee of $164 plus $18 per month for members. After how many months would the total cost at Gym A and Gym B be the same for members?

Answer:
The total charge at Gym A and Gym B would be the same at 6 months
Step-by-step explanation:
The model for the charges of both Gyms is made of the registration fee plus a variable quantity per month.
Let's call m the number of months for members.
Gym A charges $74 plus $33 per month, thus:
[tex]C_a=74+33m[/tex]
Gym B charges $164 plus $18 per month, thus:
[tex]C_b=164+18m[/tex]
We want to find out the number of months needed for both charges to be the same, thus:
[tex]74+33m=164+18m[/tex]
Subtracting 74 and 18m:
[tex]33m-18m=164-74[/tex]
Simplifying:
[tex]15m=90[/tex]
Dividing by 15:
[tex]m=90/15=6[/tex]
m=6
The total charge at Gym A and Gym B would be the same at 6 months