A golfer has two options for membership in a golf club. A social membership costs \( \$ 1775 \) in annual dues. In addition, he would pay a \( \$ 50 \) greens fee and a \( \$ 25 \) golf cart fee every time he played. A golf membership costs \( \$ 2425 \) in annual dues. With this membership, the golfer would only pay a \( \$ 25 \) golf cart fee when he played. How many times per year would the golfer need to play golf for the two options to cost the same? The golfer would need to golf

To determine how many times the golfer would need to play for the two membership costs to equalize, we can set up the equation based on the costs of each option. Let \( x \) be the number of times the golfer plays in a year. The total cost for the social membership is: \[ 1775 + 50x + 25x = 1775 + 75x. \] The total cost for the golf membership is: \[ 2425 + 25x. \] Setting the two costs equal to each other gives us: \[ 1775 + 75x = 2425 + 25x. \] Now, solve for \( x \): 1. Subtract \( 25x \) from both sides: \[ 1775 + 50x = 2425. \] 2. Subtract \( 1775 \) from both sides: \[ 50x = 650. \] 3. Divide both sides by \( 50 \): \[ x = 13. \] The golfer would need to play 13 times per year for the two options to cost the same!