You are choosing between two health clubs. Club A offers membership for a fee of \( \$ 18 \) plus a monthly fee of \( \$ 16 \). Club B offers membership for a fee of \( \$ 28 \) plus a monthly fee of \( \$ 14 \). After how many months will the total cost of each health club be the same? What will be the total cost for each club? In months the total cost of each health club will be the same.

To find out after how many months the total cost of each health club will be the same, we can set up equations for the total cost of each club. Let \( m \) be the number of months. **For Club A:** - Membership fee: \( \$ 18 \) - Monthly fee: \( \$ 16 \) The total cost for Club A after \( m \) months is: \[ \text{Total cost for Club A} = 18 + 16m \] **For Club B:** - Membership fee: \( \$ 28 \) - Monthly fee: \( \$ 14 \) The total cost for Club B after \( m \) months is: \[ \text{Total cost for Club B} = 28 + 14m \] Now, we set the total costs equal to each other to find \( m \): \[ 18 + 16m = 28 + 14m \] Next, we can solve for \( m \): 1. Subtract \( 14m \) from both sides: \[ 18 + 2m = 28 \] 2. Subtract \( 18 \) from both sides: \[ 2m = 10 \] 3. Divide by \( 2 \): \[ m = 5 \] So, the total cost of each health club will be the same after \( 5 \) months. Now, we can calculate the total cost for each club after \( 5 \) months. **Total cost for Club A after 5 months:** \[ \text{Total cost for Club A} = 18 + 16 \times 5 = 18 + 80 = 98 \] **Total cost for Club B after 5 months:** \[ \text{Total cost for Club B} = 28 + 14 \times 5 = 28 + 70 = 98 \] Thus, the total cost for each club after \( 5 \) months will be \( \$ 98 \). In summary: - The total cost of each health club will be the same after **5 months**. - The total cost for each club will be **\$ 98**.