Splitting Bill

[Leper]

Hi,

I have a problem. We have an electricity bill for $1167.80 and six of us were living here until one of us left 67 days into the 92 day billing period. I want to know how I can figure out this person's share of the bill as all of us want to ensure all is fair. My pea brain knows that I could divide the bill by six and then roughly divide one of those portions into 2/3, but then there's a third of a share not being paid. I'm very eager to know how to resolve this problem. Thank you all in advance!

 

[Harry_the_cat]

Ok there are 5 people there for 92 days and one there for 67 days. All up that is 5x92+1x67 = 527 "people days of electricity".
5 of you pay 92/527 of $1167.80 = $203.87 and the person who left pays 67/527 of $1167.80 = $148.47.
Check: 5x$203.87 + 1x$148.47 = $1167.82 (rounding error).

Alternatively, you could do what you said but multiply the last portion by 67/92 rather than 2/3 to be more exact. Then the bit not paid needs to be divided among the 5 who are left. It will work out the same.

 

[JeffM]

I am telling you a different way to get the same answer as was given to you by the world’s most intelligent feline. It may be easier to explain.

The average daily bill was [MATH]1167.80 \div 92 \approx 12.6935.[/MATH]
For 67 days, that needs to be split 6 ways.

[MATH]12.6935 \div 6 \approx 2.1156.[/MATH]
So the person who moved out needs to pay

[MATH] 67 \times 2.1156 = 141.74.[/MATH]
That leaves [MATH]1167.80 - 141.74 = 1026.06[/MATH] still to be paid.

Divide that five ways. That works out to 205.21 a person.

You will be a penny off. Flip to see who pays the extra penny.

 

[Deleted member 4993]

I am telling you a different way to get the same answer as was given to you by the world’s most intelligent feline. It may be easier to explain.

The average daily bill was [MATH]1167.80 \div 92 \approx 12.6935.[/MATH]
For 67 days, that needs to be split 6 ways.

[MATH]12.6935 \div 6 \approx 2.1156.[/MATH]
So the person who moved out needs to pay

[MATH] 67 \times 2.1156 = 141.74.[/MATH]
That leaves [MATH]1167.80 - 141.74 = 1026.06[/MATH] still to be paid.

Divide that five ways. That works out to 205.21 a person.

You will be a penny off. Flip to see who pays the extra penny.

Jeff, you and Cat do not come to the same answer.(141.74 vs. 148.47 ~ 5% difference).

Cat assumed that the average consumption went down as the sixth person moved. You have assumed that the average usage/day was same whether there was 5 person or 6 persons. That could be true for certain things - e.g. refrigerator, whole house heat/AC, etc.

 

[Steven G]

I vote for cat being correct. Its about time that Jeff made an error (and it was only a 5% error)

 

[JeffM]

I vote for cat being correct. Its about time that Jeff made an error (and it was only a 5% error)

Off to the corner with me. Too be beaten by a cat. How humbling!

 

[Deleted member 4993]

Off to the corner with me. Too be beaten by a cat. How humbling!

I would not call Jeff's assumption wrong - it is just less defensible. I suggest some time check it out yourself. Unless there are little kids involved ( those require lot of "individual" energy) - the utility bill remains constant - more or less (like say rent of an one bdrm. apt.) .

 

[Steven G]

If there are more people to turn on the lights then the lights will be turned on more often. Even you suggested that this is true!

 

[JeffM]

If there are more people to turn on the lights then the lights will be turned on more often. Even you suggested that this is true!

It depends on what time of year it was. Air conditioning raises havoc on our bill.

 

[Leper]

Thank you everyone! I appreciate the help so much. Stay safe from Covid!