help required splitting a shared utility bill...

[weedguru_animal]

If anyone has a crafty mathematical mind and can help me with the following, i'd be mightily grateful.

The gas bill is for $138.06. Over a period of 61 days.
For 61 days Mr D was living here, for 44 days Miss S was living here and for 16 of those days Mr Z was living here.

Bearing in mind, somehow?, that when only Mr D was living here, the gas usage would have been far less than when all three were in the house...

any ideas how to split this close to fairly???

[Weedguru_Fire_Inside]

I'd split it in 2 between Mr. D and Mr. Z, then take 10% from each and call that Mrs. S' share.

I think anything more would be unfair and any less would be splitting hairs.

[cutthecashflow]

For 16 of the 61 or 16 of the 44 days was Mr. Z living there?

[Weedguru Higher]

This reminds of those damn problem solving questions that I so hated in my high school math class

[weedguru_animal]

I guess I didn't make myself clear enough...though thanks for the efforts so far.

Over a period of 61 days in total: Mr D all 61 days, Miss S 44 days, and Mr Z only 16 of those days. Does that make it easier to ponder? I hope so...

[Weedguru_Fire_Inside]

Sorry dude, i mixed up Mrs. S and Mr. Z.

I certainly don't fancy working out the equation, lol. If i get time later on, i'll do the proper calculations.

[sugarstalker]

are these three the only people who shall be paying for the bill?

also, were any of these charlatans staying there at the same time, or all at different times (Mr Z and Mrs S)

I had a go and I got that:

Z = 18.66 (Mr. S)
Y = 51.33 (Miss Z)
X = 70 (Mr. D)

someone more clever than me should step up and figure it out.

ps. I did it under the assumption that Mr. S and Miss Z did not stay there at the same time.
pps. I used 60 days instead of 61, because 61 is a prime number and it would be more of a bother.

[Ikku]

Here's the way I'd do it for maximum fairness.

44/61 days is roughly 72 percent. 72 percent of 138.06 is 99.40. That 99.40 should be split evenly between D and S. (49.70 each).
16/61 days is roughly 26 percent. 26 percent of 138.06 is 35.90. That should be split evenly between all 3. (17.95 each).

The remainder should be paid solely by D.

So each person should pay
D: 70.41
S: 49.70
Z: 17.95

If as you say Z was living there at the same time as S, then it might be fair to take some of the debt away from D and S and give it to Z, but not a whole lot. Anyway this is very crude and not necessarily representative of who used how much $$ worth of gas. But it seems pretty fair to me.

[Weedguru_Fire_Inside]

I think, regardless of which one of the above suggestions you use, you won't be too far off. I'm swaying toward Ikku because i can actually see the logic that he used.

[sugarstalker]

I think, regardless of which one of the above suggestions you use, you won't be too far off. I'm swaying toward Ikku because i can actually see the logic that he used.

>:(

x+y+z=140 (I rounded it up just to make it easier)

y= 11/15x
z=4/15x

x+4/15x+11/15x=140 ->15/15x+4/15x+11/15x=140
30/15x=140 -> 2x=140 -> x=140/2
x=70


11/15*70 = y

4/15*70 = z

I also changed it from 61 to 60 days since 61 is a prime, and the only prime that's any good is Optimus

[omnific.dc]

I'm lost..

[Ikku]

Sugarstalker we have pretty much the same result. You just rounded numbers before calculating instead of after and uzed too many lettars. I liek maths

Actually the way I described it turns out to be incorrect but I think the final numbers I came up with are ok. 49.70 is ALL of what S should pay for, there's no reason to count her twice by making her pay part of the 16/61 days that Z was there since that would be making her pay twice for the same days. I think it still works out to the numbers I gave, I just didn't correct the logic description for that mistake I originally made. Fun puzzle Dan

D: 70.41
S: 49.70
Z: 17.95

[Weedguru_Fire_Inside]

Well, thank god i stuck with economics and never went for the accountancy degree i was looking at.

[Weedguru Higher]

>:(

x+y+z=140 (I rounded it up just to make it easier)

y= 11/15x
z=4/15x

x+4/15x+11/15x=140 ->15/15x+4/15x+11/15x=140
30/15x=140 -> 2x=140 -> x=140/2
x=70


11/15*70 = y




4/15*70 = z

I also changed it from 61 to 60 days since 61 is a prime, and the only prime that's any good is Optimus

Oh god, I suddenly remember hating math class even more now....

I just realized that my daughter is going to be coming home with that for homework in a year or two. Please don't ask me for help sweetheart....

[sugarstalker]

You can always turn to the forums, higher, as you can see.