Any Mathematicians?

[NStocks]

Hi,

I'm looking to split a shared utility bill, a task initially assumed to be fairly straightforward.

The bill is £155.47 and it's for a period of 31 days. (May 13th to June 13 inclusive)

The household moved in one by one over a few weeks and so the bill needs to be apportioned appropriately to the dates when each house member moved in.

My initial thoughts were to divide 155.47 by 31 days to give a day rate for the energy bill, then divide that by 4 (people):

Person 1 moved in 13th May 31 days = £38.75
Person 2 moved in 15th May = 29 days = £36.35
Person 3 moved in 31st May = 23 days £28.85
Person 4 moved in 28th May = 16 days £20.05

Total: £124.00

I then realised that between people moving in, the day rate is different. For example, for the first two days, only one person was in the house and so the day rate is 155.47/31*2 = £10.30 for the two days of living alone.

I then applied this to the remaining persons but the math still doesn't add up


17 days split evenly :
£21.31 each

Add to this the numbers below for each person that moved in earlier in the month

Plus 3 people together
Person 1 £11.70
Person 2 £11.70
Person 3 £11.70


Plus 2 people together
Person 1 £5.01
Person 2 £5.01

Plus 1 person
£10.30

Total: £140.66

Any ideas?

 

[JCoe13]

For 2 days, Person 1 is responsible for the daily rate (~£5.02). For the next 6 days, Person 1 and Person 2 are responsible for splitting that daily rate between the 2 of them. The same for once person 3 and then 4 moves in.

Results are the following:

Person 1: £57.84
Person 2: £48.81
Person 3: £34.76
Person 4: £24.06

 

[Slartibart]

13th of may till 13th of june - both days included - are not 31 days. 🤓

 

[NStocks]

13th of may till 13th of june - both days included - are not 31 days. 🤓

Ah yes, 32 days!

 

[RokinAmerica]

Everyone pays roughly 1.57 per day they stayed.

155.47/99 (total days stayed by all involved)

31 days times 1.57 = 48.67
29 = 45.53
23 = 36.11
16 = 25.12
= 155.43 each put in another penny/ round up

 

[NStocks]

For 2 days, Person 1 is responsible for the daily rate (~£5.02). For the next 6 days, Person 1 and Person 2 are responsible for splitting that daily rate between the 2 of them. The same for once person 3 and then 4 moves in.

Results are the following:

Person 1: £57.84
Person 2: £48.81
Person 3: £34.76
Person 4: £24.06

That was my thinking, but the maths above comes out to £165.47, not £155.47

 

[JCoe13]

Person 3 moved in 31st May = 23 days £28.85
Person 4 moved in 28th May = 16 days £20.05

What day did Person 4 move in?

 

[NStocks]

Everyone pays roughly 1.57 per day they stayed.

155.47/99 (total days stayed by all involved)

31 days times 1.57 = 48.67
29 = 45.53
23 = 36.11
16 = 25.12
= 155.43 each put in another penny/ round up

Thanks! This all adds up.

Could you elaborate on the /99 mathematics?

 

[NStocks]

What day did Person 4 move in?

Moved in on 28th May

 

[JCoe13]

Moved in on 28th May

Someone explained the math pretty well above about /99 and then tying days out. Only asked because unless Person 4 moved out before Person 3, the # of days seems off.

 

[RokinAmerica]

If you add up all the days total people lived there it equals 99 days. The price is set at 155.47 so 155.47/99 days equals 1.57 per day. then just times each persons amount of days by 1.57 and there it is.

 

[Mousse]

Do you have access to the daily usage? One person isn't going to use as much electricity as 4 people. The guy who moved in first got hosed. It would be easy to make a spreadsheet to calculate what everyone owes if you have access to the daily electricity usage.

 

[NStocks]

Do you have access to the daily usage? One person isn't going to use as much electricity as 4 people. The guy who moved in first got hosed. It would be easy to make a spreadsheet to calculate what everyone owes if you have access to the daily electricity usage.

I could’ve read the meter readings daily, as person 1 who first moved in. But on reflection you’re right. £5 a day for one person is a lot of energy!

 

[KaliYoni]

I would just divide the bill evenly. Then go to the pub together where Person 3 pays for 1 round, Person 2 pays for 2 rounds, and Person 1 pays for 3 rounds. Bonus: by the time you all leave, nobody is going to care about the utility bill, much less do any calculations.

 

[Apple fanboy]

I would just divide the bill evenly. Then go to the pub together where Person 3 pays for 1 round, Person 2 pays for 2 rounds, and Person 1 pays for 3 rounds. Bonus: by the time you all leave, nobody is going to care about the utility bill, much less do any calculations.

This! If you are trying to divide the first bill to the penny it doesn’t bode well for life going forward.
Person one has a girlfriend sleep over 3 nights a week. Does he pay more?
Person two goes to his girlfriend’s at weekends. Does he pay less?
Person three is a gym bunny and showers three times a day. Should they pay more?
Person four steals the milk from the fridge and never replaces the toilet roll.

So glad my house sharing days are done.

Living with Mrs AFB is different of course. We share everything done the middle. I earn all the money, she spends it!

 

[Mousse]

This! If you are trying to divide the first bill to the penny it doesn’t bode well for life going forward.

Unless you're a bean counter. This is my life. I have spent 10 hours automating a 3 minute task in Excel.🤓

Person one has a girlfriend sleep over 3 nights a week. Does he pay more?
Person two goes to his girlfriend’s at weekends. Does he pay less?
Person three is a gym bunny and showers three times a day. Should they pay more?

If you have a damn good bookkeeper, I see no problem. After a while, goodwill comes into play and you won't need to keep an exhaustive account.😉

Person four steals the milk from the fridge and never replaces the toilet roll.

Living with Mrs AFB is different of course. We share everything done the middle. I earn all the money, she spends it!

She's built up a lot of goodwill. Same with my wife; she has accrued enough goodwill with me that I can deny her nothing.

 

[Analog Kid]

If you add up all the days total people lived there it equals 99 days. The price is set at 155.47 so 155.47/99 days equals 1.57 per day. then just times each persons amount of days by 1.57 and there it is.

Yeah, this is the answer. If you convince yourself it's really 32 days, then add one day for everyone.

The problem is that while you're trying to be "fair" with this approach, you're really not. Assuming utilities are charged on a usage rate, not a fixed bill, then the consumption would have been less while only person 1 was living in the flat and more when there were 4 people so person 1 is still overpaying.

And even knowing the daily usage won't solve it because one person has a Intel i9, hair dryer and toaster oven and someone else has a buzz cut, m1 Air, and eats out.

This way lies madness. There is no "fair" way to live together. I have to second the pub strategy.

 

[Apple fanboy]

Unless you're a bean counter. This is my life. I have spent 10 hours automating a 3 minute task in Excel.🤓

If you have a damn good bookkeeper, I see no problem. After a while, goodwill comes into play and you won't need to keep an exhaustive account.😉

She's built up a lot of goodwill. Same with my wife; she has accrued enough goodwill with me that I can deny her nothing.

I spend about 8 hours a day in excel myself.

 

[James_C]

I spend about 8 hours a day in excel myself.

Snap . I have been using Excel since 1988, I hate to think how many hours I have spent in Excel.

 

[Apple fanboy]

Snap . I have been using Excel since 1988, I hate to think how many hours I have spent in Excel.

I could create a spreadsheet to work it out!

 

[compwiz1202]

For 2 days, Person 1 is responsible for the daily rate (~£5.02). For the next 6 days, Person 1 and Person 2 are responsible for splitting that daily rate between the 2 of them. The same for once person 3 and then 4 moves in.

Results are the following:

Person 1: £57.84
Person 2: £48.81
Person 3: £34.76
Person 4: £24.06

View attachment 2217685

Awesome yes had to figure the per person for each section with different numbers of people.

 

[compwiz1202]

Yeah, this is the answer. If you convince yourself it's really 32 days, then add one day for everyone.

The problem is that while you're trying to be "fair" with this approach, you're really not. Assuming utilities are charged on a usage rate, not a fixed bill, then the consumption would have been less while only person 1 was living in the flat and more when there were 4 people so person 1 is still overpaying.

And even knowing the daily usage won't solve it because one person has a Intel i9, hair dryer and toaster oven and someone else has a buzz cut, m1 Air, and eats out.

This way lies madness. There is no "fair" way to live together. I have to second the pub strategy.

Yea it would near impossible to be totally fair without monitoring each outlet and what people used. So unless someone is using something that uses an unusually high amount of power, I would just split it evenly. It would be like getting crazy and logging how long each person was home and split the rent by that.

 

[compwiz1202]

Unless you're a bean counter. This is my life. I have spent 10 hours automating a 3 minute task in Excel.🤓

But over time you will save those ten hours. Plus building macros is fun.

 

[compwiz1202]

Do you have access to the daily usage? One person isn't going to use as much electricity as 4 people. The guy who moved in first got hosed. It would be easy to make a spreadsheet to calculate what everyone owes if you have access to the daily electricity usage.

Yes especially if the heat is electric. It's going to heat four the same as one unless one is colder and keeps turning it up.