Health Club Fees You are choosing between two health clubs. Club A fee of \( \$ 20 \). Club B offers membership for a fee of \( \$ 42 \) plus a monthly fee of each health club be the same?

To determine when the total fees for both health clubs will be the same, we can set up an equation based on the information provided. Let \( x \) be the number of months you plan to be a member. For Club A, the total cost after \( x \) months is: \[ \text{Total cost for Club A} = 20 + 0 \cdot x = 20 \] (assuming there are no additional monthly fees). For Club B, the total cost after \( x \) months is: \[ \text{Total cost for Club B} = 42 + 0 \cdot x = 42 \] (again, assuming there are no additional monthly fees). However, if Club B has a monthly fee, we need to include that in the equation. Let's denote the monthly fee for Club B as \( m \). Then, the total cost for Club B after \( x \) months would be: \[ \text{Total cost for Club B} = 42 + mx \] To find out when the costs are equal, we set the two total costs equal to each other: \[ 20 + 0 \cdot x = 42 + mx \] Since Club A has no monthly fee, we can simplify this to: \[ 20 = 42 + mx \] Now, we can solve for \( x \): \[ mx = 20 - 42 \] \[ mx = -22 \] This equation indicates that for the costs to be equal, the monthly fee \( m \) must be negative, which is not possible in a real-world scenario. Therefore, Club A will always be cheaper than Club B unless Club B has a monthly fee that is significantly lower than the initial fee of Club A. If you provide the monthly fee for Club B, we can find the exact number of months where the costs would be equal.