How Does the Cost Per Person Change with Fewer Passengers on a Charter Flight?

[zak100]

Homework Statement

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?

Homework Equations

ThirtySixCost = 36 * (costPerPerson + 12)
FixedCost = NumberofPersons * costPerPerson (Note if NumberofPersons>40)

Not sure about the correctness of equations

The Attempt at a Solution

I don't know how to solve it because data is incomplete.
ThirtySixCost=?
FortyCost=?

Somebody please guide me how to solve it.

Zulfi.
[/B]

 

[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.

 

[zak100]

Hi,
Please tell me how to find costPerPerson?

Zulfi.

 

[Mark44]

Homework Statement

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?

Homework Equations

ThirtySixCost = 36 * (costPerPerson + 12)
FixedCost = NumberofPersons * costPerPerson (Note if NumberofPersons>40)

Not sure about the correctness of equations

The Attempt at a Solution

I don't know how to solve it because data is incomplete.
ThirtySixCost=?
FortyCost=?[/B]

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.

 

[zak100]

Hi,
FTC = Fixed Total Cost
CPP = Cost Per Person
CPP = FTC + 12

I can form only one equation. Please guide me.

Zulfi.

 

[scottdave]

Hi,
FTC = Fixed Total Cost
CPP = Cost Per Person
CPP = FTC + 12

I can form only one equation. Please guide me.

Zulfi.

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.

 

[Mark44]

FTC = Fixed Total Cost
CPP = Cost Per Person
CPP = FTC + 12

The last equation makes no sense. You are saying that the cost for one person is $12 more than the fixed cost.

 

[zak100]

Hi,
Mr. scottdave:
Do you mean this:CPPThirtySix = CPPForty + 12

Zulfi.

 

[scottdave]

Hi,

CPPThirtySix = CPPForty + 12

Zulfi.

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

 

[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

Thanks everybody for your cooperation.

Zulfi.