# Thread: Intermediate Algebra Problem - Power Bill

1. ## Intermediate Algebra Problem - Power Bill

Hello,

I have a math problem in relation to my power bill. My power bill for the last two months was $277.17 , I split this bill with two other girls. However, I only lived at the house for one month. Hannah only lived at the house or a month and two weeks, and Brianna lived at the house for the full two months. The average power usage per day over the two months was$3.63. Based on all of this, how much should each person pay towards the power bill?

2. Originally Posted by sarajane
Hello,

My power bill for the last two months was $277.17 ... The average power usage per day over the two months was$3.63.
277.17 / 62 = 4.47

3. Your task is to QUANTIZE the bill down to the smallest necessary unit.

1 Year = 52 Weeks = 12 Months, thus 1 Month = 4.33333333 weeks

In your two months you have 8.6666666 weeks.

You lived in it for a month. You get 4.3333333 weeks
MoveOut for 1 month & 2 Weeks. She gets 6.33333 weeks
Legacy has both months. She gets 8.666666 weeks.

Total weeks lived? 4.3333333 + 6.3333333 + 8.666666 = 19.3333333
Charge You: 4.3333 / 19.33333 = 22.4%
ChargeMoveOut: 6.333333 / 19.333333 = 32.8%
Charge Legacy: 8.666666 / 19.333333 = 44.8%

Check: 22.4 + 32.8 + 44.8 = 100.0 Check!

Now, if one is a dope and keeps leaving the door open while running the air conditioner, this might change the EVEN calculation demonstrated.

For future reference, upgrade those math skills so that you can SHOW us YOUR solution. You could charge the others for the trouble of doing the calculation.
You: 22.4% - $10.00 MoveOut: 32.8% +$5
Legacy:44.8% + $5 Something like that. Don't you DARE charge for ME ding the calculations. I leave it to you to figure out how to apply the percentages to the total bill. 4. Originally Posted by Denis 277.17 / 62 = 4.47 Please check your post for typo's.... The power company stated that the average usage per day was$3.63, I didn't do any calculations, but I understand your confusion.

Thank you tkhunny!

5. Certainly you can use DAYS, rather then WEEKS. Should be close to the same.

(How many day were you there?) divided by (How many life-days were in the period?) - Multiply this percentage by the total bill for all participants.
A "life-day" is one day lived in the apartment. For example, if there were two on the first day, that's TWO life-days for every actual day. If there were three living in the apartment at the beginning of month #2, that would be THREE life-days for every actual day.

OR

How many days were TWO present? Split that 50/50 amongst the two that were present. There may be a discrepancy of $0.01, due to rounding. Just settle it and pay that yourself. How many days were THREE present? Split that 33.333/33.333/33.334 amongst the three that were present. This almost never comes out even. Again, you pay the extra couple cents and stay friends. 6. Originally Posted by sarajane The power company stated that the average usage per day was$3.63, I didn't do any calculations, but I understand your confusion.

Thank you tkhunny!
The power bill generally constitutes of power usage charge + surcharges (e.g. distribution charge, taxes, etc.). I believe that is why this ~0.80 $/day extra charge. I would use tkhunny's method and distribute the charges as percentage. Otherwise calculation can become convoluted. 7. Make the total invoice$288
2 months = 8 weeks

Sara Jane: 4 weeks
Hannah: 6 weeks
Brianna: 8 weeks

Total weekly periods: 4+6+8 = 18

Sara Jane: 4/18 = 64
Hannah: 6/18 = 96
Brianna: 8/18 = 128

64+96+128 = 288

And everybody lived happily forever after...

8. Originally Posted by Denis
Make the total invoice \$288
2 months = 8 weeks

Sara Jane: 4 weeks
Hannah: 6 weeks
Brianna: 8 weeks

Total weekly periods: 4+6+8 = 18

Sara Jane: 4/18 = 64
Hannah: 6/18 = 96
Brianna: 8/18 = 128

64+96+128 = 288

And everybody lived happily forever after...
Well, sure, but that looks too easy and you probably can't charge or your efforts.

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