Final answer:
To determine after how many months the total cost for each health club will be the same, use the equation x + n(dx) = y + n(dy), where x is the monthly cost of Health Club A, y is the monthly cost of Health Club B, dx is the rate of change of cost per month for Health Club A, and dy is the rate of change of cost per month for Health Club B.
Step-by-step explanation:
To determine after how many months the total cost for each health club will be the same, we can use a mathematical formula. Let's assume that Health Club A has a monthly cost of $x and Health Club B has a monthly cost of $y. We can set up an equation to find the number of months (n) such that the cost for both clubs is equal:
x + n(dx) = y + n(dy)
where dx is the rate of change of cost per month for Health Club A and dy is the rate of change of cost per month for Health Club B. Solving this equation will give us the value of n, which represents the number of months it will take for the total cost to be the same for both health clubs.