# Fixed Cost & Cost Per Person

1. Jul 10, 2017

### zak100

1. The problem statement, all variables and given/known data
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? 2. Relevant equations ThirtySixCost = 36 * (costPerPerson + 12) FixedCost = NumberofPersons * costPerPerson (Note if NumberofPersons>40) Not sure about the correctness of equations 3. The attempt at a solution I dont know how to solve it because data is incomplete. ThirtySixCost=? FortyCost=? Somebody please guide me how to solve it. Zulfi. 2. Jul 10, 2017 ### scottdave Reread the problem statement. Your costPerPerson represents the cost per person, when there are 40 people. Your ThirtySixCost is the total cost to rent the plane (but that is a Fixed cost). I did not see anything about greater than 40. You can get to 3 equations and 3 unknowns to solve it. For example (not real numbers), if it costs$360 to rent something (say a lake house), then for 40 people, that is $9 per person, but for 36 people it is$10 per person. It costs $1 more per person if you only have 36 people. Last edited: Jul 10, 2017 3. Jul 11, 2017 ### zak100 Hi, Please tell me how to find costPerPerson? Zulfi. 4. Jul 11, 2017 ### Mark44 ### Staff: Mentor These variable names aren't useful. The fixed cost is the same whether there are 40 people or 36 people. Let x = the cost per person with 40 passengers. Let f = the fixed cost of chartering the airplane. • Write an expression that represents the cost per person with 36 passengers. (Use the information given in the problem.) • Translate the 2nd sentence in the problem statement into an algebraic equation. 5. Jul 11, 2017 ### zak100 Hi, FTC = Fixed Total Cost CPP = Cost Per Person CPP = FTC + 12 I can form only one equation. Please guide me. Zulfi. 6. Jul 11, 2017 ### scottdave The plane costs an amount (call it FTC), whether there is 1 passenger or 36 passenger or 40 passengers. The cost per person depends on the fixed cost (which does not change, and the number of passengers. How about this?: FTC is total fixed cost. CPPForty = FTC / 40. CPPthirtysix = FTC / 36. The problem statement gives you another relationship between CPPForty and CPPthirtysix, which you can make another equation. You may want to re-look at the example problem I posed in post #2, to see how you can relate your problem to that one. 7. Jul 11, 2017 ### Mark44 ### Staff: Mentor The last equation makes no sense. You are saying that the cost for one person is$12 more than the fixed cost.

8. Jul 11, 2017

### zak100

Hi,
Mr. scottdave:
Do you mean this:

CPPThirtySix = CPPForty + 12

Zulfi.

9. Jul 11, 2017

### scottdave

Yes, now with 3 equations you should be able to solve for CPPThirtySix, CPPForty and FTC.

10. Jul 12, 2017

### zak100

Hi,
I am able to solve it.
CP36 = FTC/36 ---(1)
CP40 = FTC/40 ---(2)
CP36 = CP40 + 12--- (3)
After solving these eq., i am able to get correct answer:
CP40 = 108
CP36 = 120 (Not required in the question)
FTC = 4320