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Fixed Cost & Cost Per Person

  1. Jul 10, 2017 #1
    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.

    Somebody please guide me how to solve it.

  2. jcsd
  3. Jul 10, 2017 #2


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    Homework Helper
    Gold Member

    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
  4. Jul 11, 2017 #3
    Please tell me how to find costPerPerson?

  5. Jul 11, 2017 #4


    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.
  6. Jul 11, 2017 #5
    FTC = Fixed Total Cost
    CPP = Cost Per Person
    CPP = FTC + 12

    I can form only one equation. Please guide me.

  7. Jul 11, 2017 #6


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    Gold Member

    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.
  8. Jul 11, 2017 #7


    Staff: Mentor

    The last equation makes no sense. You are saying that the cost for one person is $12 more than the fixed cost.
  9. Jul 11, 2017 #8
    Mr. scottdave:
    Do you mean this:

    CPPThirtySix = CPPForty + 12

  10. Jul 11, 2017 #9


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    Yes, now with 3 equations you should be able to solve for CPPThirtySix, CPPForty and FTC.
  11. Jul 12, 2017 #10
    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

    Thanks everybody for your cooperation.

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