A group can charter a particular aircraft at a fixed total c

A group can charter a particular aircraft at a fixed total cost. If 36 people charter the aircraft rather than 40 people, then the cost per person is greater by 12$.

A) What is the fixed total cost to charter the aircraft?

B) What is the cost per person if 40 people charter the aircraft?

Please show all work and note any information (if necessary) you used to come up with the answer.

Solution

Let the fixed total cost of the aircraft charter be $ x.

Then, if 40 people charter the aircraft, the cost per person is x/40 and if 36 people charter the aircraft, the cost per person is x/36.

Then x/36 = x/40 + 12 . On multiplying both the sides by 360 (LCM of 36 and 40), we get 10x = 9x + 4320 or, 10x -9x = 4320 so that x = 4320.

Thus, the fixed cost of the charter of the aircraft is $ 4320.

Also, the cost per person, if 40 people charter the aircraft is $ 4320/40 = $ 108.