It will take 4 months for the total amount of money paid to both gyms to be the same.
We would apply the knowledge of world problem to create equations in order to solve the problem given as shown below:
Equation for total amount (t) Planet Fitness charges:
Membership fee (initial value) = $65
Monthly fee = $25
Let x represent the number of months
Therefore:
[tex]t = 25x + 65[/tex]
Equation for total amount (t) Crunch Fitness charges:
Membership fee (initial value) = $105
Monthly fee = $15
Let x represent the number of months
Therefore:
[tex]t = 15x + 105[/tex]
To find the total number of months (x) for both gyms to have the same total amount of money paid, set the algebraic equations of both equal to each other and solve for x:
Thus:
[tex]25x + 65 = 15x + 105[/tex]
Collect like terms
[tex]25x - 15x = - 65 + 105\\10x = 40[/tex]
Divide both sides by 10
[tex]x = 4[/tex]
Therefore, for both gyms to have the same total amount paid to them, it will take 4 months.
Learn more about world problem here:
https://brainly.com/question/16889590
