My Math Forum Working out electricity bill

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 September 14th, 2012, 01:24 PM #1 Newbie   Joined: Sep 2012 Posts: 3 Thanks: 0 Working out electricity bill Hi. I am struggling with working out the shared electricity bill for my apartment. Three people live in the apartment. The bill is for £298.58. On March 16th, my sister and I moved in. On May 14th, the other tenant moved in. The bill ends on August 20th. Currently I have the bill worked out at £113.38 for the period me and my sister lived together and then £185.20 for the period from when our roommate moved in to the end of the bill on August 20th. I then divided the first number for when just my sister and I lived here in two and then the other number for the period all three of us have lived here in three. That means £56.69 each for my sister and I for the when just the two of us lived here and then £61.73 each for the three of us for when we all lived here. The numbers work out but the problem is that's not right because surely we have been using more electricity with the three of us living here than when just the two were living here. The first period for when just my sister and I lived here lasted for 59 days. It was 99 days from when our roomate moved in to the end of the bill. My current calculations mean that my sister and I would be paying nearly double to what our roommate is paying. As my sister suggested when I started to work this out, surely that isn't right. Firstly it was eight weeks and three days between when we moved in and then 14 weeks from when our roommate moved in until the end of the bill. I asked the electricity company for a seperate bill for when just my sister and I lived here and then another for when the three of us have been living here. They said it wasn't possible. It occurred to me that this is basically a math(s) problem. That's what brought me here. Given that three people would be using more electricity collectively and that the period of time for when three of us have been living here is almost double of when just my sister and I lived here, should my sister and I be paying basically double what our roommate is paying? What would a fair share be? Sorry if you guys don't like asking questions from people from people who aren't usually on the board. If you are ok with it, apologies if it is posted in the wrong forum. If it makes is easier, as I am sure it would, just round up the total to 300. If you guys can work this out, can you explain it simple terms, as I am not a math(s) expert. Thanks.
 September 14th, 2012, 01:58 PM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Working out electricity bill Let me see if I understand: you have a bill of £298.58 but no information about when electricity was used. One person lived there for 60 days, while the other two lived there for 158 days. If you don't use air conditioning, I think that electricity usage is pretty much a flat amount per person. In that case the most reasonable method is to have the two pay a 158/(2*158+60)-th share of the bill each, while the other pays a 60/(2*158+60)-th share of the bill. That would be £125.47 and £47.65, respectively. If you do use air conditioning or something else which affects the whole house and does not change much per person, estimate how much that used over the whole time and divide that up separately. Say you used £100 worth of air conditioning. Then it would be reasonable to charge 98/158-th to the two (hence 49/158-th for each) and 60/198-th to the three (hence 20/158-th for each) for a total of £43.67 and £12.65 respectively. Then divide up the remaining £198.58 as above. (As always, check for arithmetic errors and the like.)
 September 14th, 2012, 07:47 PM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 Re: Working out electricity bill Tell the intruder to pay 1/3 of the total bill...else you'll kick him out
September 14th, 2012, 10:35 PM   #4
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Re: Working out electricity bill

Quote:
 Originally Posted by Denis Tell the intruder to pay 1/3 of the total bill...else you'll kick him out
http://school.maths.uwa.edu.au/~berwin/ ... timidation ... I like it.

September 15th, 2012, 12:35 AM   #5
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Re: Working out electricity bill

Quote:
 Originally Posted by CRGreathouse Let me see if I understand: you have a bill of £298.58 but no information about when electricity was used. One person lived there for 60 days, while the other two lived there for 158 days. If you don't use air conditioning, I think that electricity usage is pretty much a flat amount per person. In that case the most reasonable method is to have the two pay a 158/(2*158+60)-th share of the bill each, while the other pays a 60/(2*158+60)-th share of the bill. That would be £125.47 and £47.65, respectively. If you do use air conditioning or something else which affects the whole house and does not change much per person, estimate how much that used over the whole time and divide that up separately. Say you used £100 worth of air conditioning. Then it would be reasonable to charge 98/158-th to the two (hence 49/158-th for each) and 60/198-th to the three (hence 20/158-th for each) for a total of £43.67 and £12.65 respectively. Then divide up the remaining £198.58 as above. (As always, check for arithmetic errors and the like.)
Thanks for your help, I'll work it out eventually.

September 15th, 2012, 12:37 AM   #6
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Re: Working out electricity bill

Quote:
 Originally Posted by CRGreathouse Let me see if I understand: you have a bill of £298.58 but no information about when electricity was used. One person lived there for 60 days, while the other two lived there for 158 days. If you don't use air conditioning, I think that electricity usage is pretty much a flat amount per person. In that case the most reasonable method is to have the two pay a 158/(2*158+60)-th share of the bill each, while the other pays a 60/(2*158+60)-th share of the bill. That would be £125.47 and £47.65, respectively. If you do use air conditioning or something else which affects the whole house and does not change much per person, estimate how much that used over the whole time and divide that up separately. Say you used £100 worth of air conditioning. Then it would be reasonable to charge 98/158-th to the two (hence 49/158-th for each) and 60/198-th to the three (hence 20/158-th for each) for a total of £43.67 and £12.65 respectively. Then divide up the remaining £198.58 as above. (As always, check for arithmetic errors and the like.)
What does 'th' mean in your group of second equations?

September 15th, 2012, 05:20 PM   #7
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Re: Working out electricity bill

Quote:
 Originally Posted by achtungbaby What does 'th' mean in your group of second equations?
It's just the same as the "th" in "fifth" or "one-seventh". That gives the fraction of the whole assigned to the person, not the number of pounds.

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# how to work out the equation for utilities bills among roommates

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