Without specific fee structures for Kings gym and Reds gym, it is not possible to calculate the number of months where the two gyms will cost the same. Normally, with the right data, you would set up an equation for the total cost over time for both and solve for the variable m.
To determine how many months, m, it will take for the costs at Kings gym and Reds gym to be the same, we must be provided with or derive a mathematical relationship for the cost over time for both gyms. Since there are no specific fee structures given in the question, we cannot perform an exact calculation. Normally, you would set up an equation where the total cost over time for Kings gym equals the total cost over time for Reds gym, solving for the variable m (months). This would normally involve fixed costs (like initial membership fees) and variable costs (monthly rates), and perhaps any promotional offers that may be in effect for a certain number of initial months.
Without this data, we can't determine the exact month where the fees would be equal. However, you can find the answer by setting up the equation once you have the necessary fee details for each gym. Generally, you would obtain the monthly fee and any initial fee for both gyms and set the total costs equal to each other to solve for m.
Conclusion: To find the number of months where Kings gym and Reds gym cost the same, one would typically use the monthly fee information and any initial fees, set the total costs to be equal, and solve for m. Unfortunately, in this case, insufficient information is given to provide a concrete final answer .