Question

"An automobile company is sponsoring a charity golf tournament to raise money for a charity. There are two possible venues:
RTJ Golf Resort, which charges a fixed rental cost of $7,100 plus an additional fee of $98 per person. The automobile company will charge $320 per ticket if the event is at RTJ Golf Resort.
Wynlakes Golf & Country Club, which charges a fixed rental cost of $2,700 plus $130 per person. The automobile company will charge $275 per ticket if the event is at Wynlakes.
The automobile company will also have $2,000 in costs for administration, marketing, and entertainment at both venues. What is the fewest number of tickets to be sold for the company to be indifferent between the two venues? (Your answer can be a decimal number.)"

Answer 1

Let the number of tickets be x

RTJ Golf Resort

Cost when booking = 7100(fixed cost) + 98x

Revenue = 320x

Profit = 320x - 7100 - 98x

Wynlakes Golf

Cost when booking = 2700(fixed cost) + 130x

Revenue = 275x

Profit = 275x - 2700 - 130x

The automobile company will be indifferent between the two venues the profit from both is equal. Hence

320x - 7100 - 98x = 275x - 2700 - 130x

222x - 7100 = 145x - 2700

77x = 4400

x = 57.14. This is the fewest number of tickets to be sold for the company to be indifferent between the two venues.