Hi,
I have got a following question:

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?


I am not able to form the correct eq. I have developed the following equations:
ExceededCost = 36 * (costPerPerson + 12)
FixedCost = NumberofPersons * costPerPerson


Some body please guide me if the above equations are correct or not.

Zulfi.

 

This is a question on how to apply algebra to problem solving.

Ask yourself "What are the unknowns?"
The unknown is the fixed total cost. Give this a variable such as T.

What is the cost per person?
See if you can take it from there.

 

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

I can form only one equation. Please guide me.

Zulfi.

 

Think of two ways to write down the total cost. (Even this is probably too mutch of a clue.)

Les.

 

If FTC = Fixed Total Cost
and there are N persons,
write out the equation for CPP, Cost Per Person.

 

If FTC = Fixed Total Cost
and there are N persons,
write out the equation for CPP, Cost Per Person.

CPP = FTC/N
CPPThirtySix = FTC/36
CPPForty = FTC/40
CPPThirtySix = FTC/40 + 12

Four unknowns & 3 eq. We need one more eq.

Zulfi.

 

CPP = FTC/N

Zulfi.

Good.
Now, there are two values of N,
N1 and N2

Show two equations, for CPP1 and CPP2.

 

Hi,
I have already shown CPPForty and CPPThirtySix, what else are you talking about?

Thanks for your guidance.

Zulfi.

 

Hi,
I have already shown CPPForty and CPPThirtySix, what else are you talking about?

Thanks for your guidance.

Zulfi.

You have arrived at
CPP = FTC/N

Now write two new equations for N1 and CPP1, and N2 and CPP2.

If you cannot see this you are not getting it.

btw: there are not four unknowns. There is only one unknown, FTC. You only need one equation.

 

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

I can form only one equation. Please guide me.

Zulfi.

You need to give some thought to your terms and equations.

The Fixed Total Cost is the entire cost to charter the aircraft. So it might be $20,000.

The Cost Per Person is how much it costs per person (hence the name) on the aircraft.

So does it REALLY make sense to say that

CPP = FTC + 12

Try putting some numbers and working it backwards and then try to turn it around.

An airplane can be leased for $20,000

If 20 people split the cost, how much does it cost each of them?

If 25 people split the cost, how much does it cost each of them?

How much more does it cost each person if there are only 20 compared to if there are 25?

Try to write an expression that answers that last question in terms of the three values from the prior three statements. Then simply solve for the total lease cost.

 

CPP = FTC/N
CPPThirtySix = FTC/36
CPPForty = FTC/40
CPPThirtySix = FTC/40 + 12

Four unknowns & 3 eq. We need one more eq.

Zulfi.

Sure looks like four equations to me. But that's doing things the hard way.

I see my prior post is OBE (overtaken by events)

You have two different equations for CPPThirtySix.

What do you know has to be true of those two equations?

 

From your first post what do you know about the relationship between ExceededCost and FixedCost ?

Les.

 

The task is not for electronics and therefore I will show liberty.
No algebra is needed.
If 36 people, then all they overpay 36 * 12 = 432. This money is paid (40-36) = 4 people. Then one person (1 of 40) pays 432/4 = 108.

 

Hi,
Bordodynov, thanks for your smart solution. I have to solve the 3 equation simultaneously.
My solution is:
FTC = Fixed Total Cost
CP36 = Cost per person36 = FTC/36 ---(1)
CP40 = Cost per person40 = FTC/40 ---(2)
CP36 = CP40 + 12--- (3)


Putting CP40 from (2) into (3)

CP36 = FTC/40 + 12 ---- (4)

From (1)

FTC = 36 * CP36

Putting FTC value in (4)

CP36 = (36 * CP36)/40 + 12

CP36 = (36CP36 + 480)/40

40CP36 – 36CP36 = 480

CP36 = 120

Putting CP36 in (3)

120 – 12 = CP40

CP40 = 108

Putting CP40 in (2)

108 = FTC/40

FTC = 4320
Thanks everybody for your cooperation and guidance.
Zulfi.

 

Now that you have worked out the solution, here is how I would have done it in one equation:

FTC/36 - FTC/40 = 12

Solve for FTC

 

Hi,
Great. God bless you.

Zulfi.

 

You were close in your first post

ExceededCost = 36 * (costPerPerson + 12)
FixedCost = NumberofPersons * costPerPerson

ExceededCost and FixedCost are the same thing (As this is the cost of chartering the flight.)
.
If you replaced NumberofPersons with the value of 40 (As you know that with that number the cost per person is 12$ less than with 36 persons)
As the left hand side of the two equations is the same thing then the value of the right hand side of the equations is the same. So we can now write it down as a single equation.
36 * (costPerPerson + 12) = 40 * costPerPerson
We can rearange this as
36 * costPerPerson + 36 * 12 = 40 * costPerPerson
If we rearange it again we get
36 * 12 = (40 * costPerPerson) - (36 * costPerPerson )
Which is
36 * 12 = 4 * costPerPerson
432 = 4 * costPerPerson
So
costPerPerson = 432/4 (= 108)
So the charter price is 40 * 108 = 4320
As with 36 people the cost per person is 108 +12 = 120
And 120 * 36 = 4320

Les.

 

Hi,
Thanks for your information and work. Sorry no body told me that my equations were correct.

Zulfi.

 

CPP = FTC/N
CPPThirtySix = FTC/36
CPPForty = FTC/40
CPPThirtySix = FTC/40 + 12

Four unknowns & 3 eq. We need one more eq.

Zulfi.

You had two important equations in post #6:

CPPThirtySix = FTC/36
CPPThirtySix = FTC/40 + 12

This gives:
FTC/36 = FTC/40 + 12

with one unknown.