Final answer:
It would take 9 months for each gym to cost the same amount of money.
Step-by-step explanation:
To find out how many months it would take for each gym to cost the same amount of money, we can set up an equation. Let's denote the number of months as 'm'. The total cost for the first gym would be $24m + $135 since there is a joining fee. The total cost for the second gym would be $39m since there is no joining fee. We can set up the equation: $24m + $135 = $39m.
To solve for 'm', we can first subtract $24m from both sides of the equation to eliminate the variable on one side. This gives us: $135 = $15m. Then, we divide both sides by $15 to solve for 'm'. The equation becomes: m = $135/$15 = 9.
Therefore, it would take 9 months for each gym to cost the same amount of money.