12. John is comparing the cost of two monthly gym memberships. Gym A charges a \( \$ 50 \) fee to join plus \( \$ 25 \) per month. Gym B charges a \( \$ 30 \) fee to join plus \( \$ 27.50 \) per month. After how many months will the cost of Gym A's membership be the same as Gym B's membership?

To determine after how many months the cost of Gym A's membership will be the same as Gym B's membership, we can set up the following equation based on their pricing structures: - **Gym A:** - **Joining Fee:** \$50 - **Monthly Fee:** \$25 - **Total Cost after \( m \) months:** \( 50 + 25m \) - **Gym B:** - **Joining Fee:** \$30 - **Monthly Fee:** \$27.50 - **Total Cost after \( m \) months:** \( 30 + 27.5m \) Set the total costs equal to each other and solve for \( m \): \[ 50 + 25m = 30 + 27.5m \] Subtract \( 25m \) from both sides: \[ 50 = 30 + 2.5m \] Subtract 30 from both sides: \[ 20 = 2.5m \] Divide both sides by 2.5: \[ m = \frac{20}{2.5} = 8 \] **Answer:** After **8 months**, the cost of Gym A's membership will equal the cost of Gym B's membership.