Question

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 1

The total charge at Gym A and Gym B would be the same at 6 months

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:

`C_a=74+33m`

Gym B charges $164 plus $18 per month, thus:

`C_b=164+18m`

We want to find out the number of months needed for both charges to be the same, thus:

`74+33m=164+18m`

Subtracting 74 and 18m:

`33m-18m=164-74`

Simplifying:

`15m=90`

Dividing by 15:

`m=90/15=6`

m=6

The total charge at Gym A and Gym B would be the same at 6 months