Maths puzzle!

[b2dan]

Just a quick one for the maths geniuses! Someone at works given me this to work out:

A motorists annual expenditure is partly constant and partly variable for the distance travelled. The cost for 500km is £50 and 6000km is £55. Find the cost for 8000km.

So far I've got 61.9!!

b2

[noodleman]

You can't answer that.

[blindswelledrat]

THats not a maths puzzle, its the ramblings of a madman

[jamesson]

What a stupid question. My answer is £255.

[Benzman]

What car can do 5,500 kms for a fiver?

[b2dan]

blindswelledrat said:

THats not a maths puzzle, its the ramblings of a madman

So you've met the chap in question!!

[TotalControl]

Doesn't make sense to me.

[AndrewTait]

56.81

There is a difference in cost of 5 between 500KM and 6000KM, and a difference in KM of 5500. 5/5500 is 0.000905 per KM.

Multiply that by 2000 (the difference between 6000 and 8000 KM) gives you 1.81, which is the cost of doing the additional 2000KM. Add this to the 55 it cost to do the original 6000KM which also includes the fixed costs gives you 56.81

The static costs will remain the same, and therefore you do not need to know what they are, but 500*0.000905 gives you 0.45 for the cost of travelling 500KM, take this away from the 50 total cost to travel 500KM gives you 49.55 fixed costs.

(Rounding errors will be in there somewhere I am sure!)

ETA - Can you show me where I can get a car that will do 2000KM on 1.81 worth of juice, please, pretty please!!!

Edited by AndrewTait on Wednesday 29th September 09:15

[JayBM]

AndrewTait said:

56.81

There is a difference in cost of 5 between 500KM and 6000KM, and a differenc in KM of 5500. 5/5500 is 0.000905 per KM.

Multiply that by 2000 (the difference between 6000 and 8000 KM) gives you 1.81, which is the cost of doing the additional 2000KM. Add this to the 55 it cost to do the original 6000KM which also includes the fixed costs gives you 56.81

The static costs will remain the same, and therefore you do not need to know what they are, but 500*0.000905 gives you 0.45 for the cost of travelling 500KM, take this away from the 50 total cost to travel 500KM gives you 49.55 fixed costs.

Yep what Andrew said, need to use substitution equations to solve, i.e.:

50 = 500x + y
55 = 6000x + y

Where X is your £/mile and y is the fixed cost.

So if you rearrange 50 = 500x + y you get:

y = 50 - 500x

If you then substitute this into the second formula you get:

55 = 6000x + (50 - 500x); which simplifies to:

55 = 5500x + 50; which gives:
x = 0.000905

If you then but the x value back into either formula you get y = 49.55.

Edited by JayBM on Wednesday 29th September 09:18

[julian64]

Expenditure = miles.x + y

where x is cost per mile and y is fixed cost

so

50 = 500x+y
55 = 6000x+y

simple substitution

gives

x (cost per mile) = .00091
y (fixed cost) = 49.55

[ZOLLAR]

My Brain hurts.......

[b2dan]

Cheers.

I'd managed to solve it by turning the statement into two equations.

I'd got the same answer as everyone else.

Cheers

Dan

[Rich135]

It is indeed £56.81 (82 if we are rounding up).

[spikeyhead]

one for us geniuses? or possibly even genii?

that, my dear OP is trivial.

Nothing more than some simple algebra.

Call that a puzzle!!!

pffft.

[anonymous-user]

Yeah I totally had that solved but seeing as everyone else had posted already I thought it would be a waste of time, uh huh

[MikeO996]

AndrewTait said:

The static costs will remain the same, and therefore you do not need to know what they are,

Edited by AndrewTait on Wednesday 29th September 09:15

Aren't you assuming that the constant costs all appear at the beginning? How do you know that they don't occur every 7000km (like a service or something)? This doesn't sound like a constant cost, more like a one off that appears at the beginng and doesn't reoccur.

I don't doubt that the maths are right, but why it looks impossible is that it's presented as a real life problem and in real life you would never solve it like this. I suspect that you should make your assumptions explicit - but what do I know, I'm not a mathemetician

Edited by MikeO996 on Wednesday 29th September 13:19

Edited by MikeO996 on Wednesday 29th September 13:22

[Frankeh]

The answer is that no car can do that kind of mileage. - PH

[AndrewTait]

MikeO996 said:

AndrewTait said:

The static costs will remain the same, and therefore you do not need to know what they are,

Edited by AndrewTait on Wednesday 29th September 09:15

Aren't you assuming that the constant costs all appear at the beginning? How do you know that they don't occur every 7000km (like a service or something)? This doesn't sound like a constant cost, more like a one off that appears at the beginng and doesn't reoccur.

I don't doubt that the maths are right, but why it looks impossible is that it's presented as a real life problem and in real life you would never solve it like this. I suspect that you should make your assumptions explicit - but what do I know, I'm not a mathemetician

Edited by MikeO996 on Wednesday 29th September 13:19

Edited by MikeO996 on Wednesday 29th September 13:22

Servicing costs are not static, as they are based on the milage you travel. For instance, a 7000KM service may not be the same cost as say a 20000KM service.

The static costs are the costs you would pay even if you did not travel any milage, for instance, purchase price of the car, tax, insurance, etc. all of which you would have to pay if you potentially wanted to use the car. These costs would remain the same if you drove 0KM, 1KM, 500KM, 6000KM, 8000KM, 20000KM.

However, generally speaking, people will spread this cost over the distance travelled, in order to look at running costs. However, the question was not "what is the running costs for travelling 8000KM", just "what it would cost to travel 8000, given the costs for 500KM, 6000KM, some of which is a static cost" Also, nowhere in the question does it say that the cost per KM does not include servicing costs averaged out over the distance travelled.

Edited by AndrewTait on Wednesday 29th September 14:39

Edited by AndrewTait on Wednesday 29th September 14:41

[b2dan]

Ironically I've just started the first day of my part time HNC/FdEng and hopefully BEng course and we've got 4 weeks of maths & engineering science. Todays lectures/tutorials were on algebra.

I never thought I'd touch the stuff again when I left secondary school!

b2

[Famous Graham]

Aren't you all assuming a linear progression?