Question

Peter owns a hotel. He has found that when he charges $119 for a night’s stay, the average occupancy is 372 people. In addition, Peter has found that with every $15 increase in the nightly cost, the hotel occupancy decreases by an average of 25. Write an expression to represent the nightly cost with x $15 price increases.

Answer 1

Without price increase,
Cost/night = $119
Average occupancy = 372
The revenue will be 119*372 = $44,268

For every $15 price increase, the occupancy decreases by 25.
Therefore with x price increases,
Cost/night = $119 + 15x
Occupancy = 372 - 25x
The revenue will be $(119 + 15x)*(372 - 25x)

Answer:
The nightly cost with x $15 price increases is $119 + 15x.