Question

Community Gym charges $60 membership fee and a $70 monthly fee. Workout Gym charges $210 membership fee and a $60 monthly fee. After how many months will the total amount of money paid to both gyms be the same? What will the amount be?

Answer 1

Mathematical Models

We will create a model for the amount of money paid at each Gym, according to the data provided in the question.

Community Gym charges a fixed $60 membership fee and $70 per month.

If we call x to the number of months, then the equation that models the charges of this Gym is:

Cc = 60 + 70x

Workout Gym charges a fixed fee of $210 and a monthly fee of $60, thus the model is:

Cw = 210 + 60x

We need to find the number of months that need to pass before both gyms charge the same. That can be calculated by equating both models:

60 + 70x = 210 + 60x

Subtracting 60:

70x = 210 + 60x - 60

Subtracting 60x:

70x - 60x = 210 - 60

Operating:

10x = 150

Dividing by 10:

x = 15

After 15 months both Gyms will have charged the same amount.

Finally, let's calculate the amount by substituting the value of x=15 in any of the models.

Cc = 60 + 70*15 = $1110

Cw = 210 + 60*15 = $1110

It can be seen both gyms have charged the same amount