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Here is a real-world math problem that I am trying to find a solution. It's kind of similar to Real life water bill problem (want to check myself), but with some additional stuffs.

We have 8 apartments in our community and we want to find out the water usage cost for each apartment and for each person.

Example:

  • Total Apartments : 8
  • Total Cost : 10000 INR

Simplest approach would be to divide total cost with total apartments. But the cost should be proportionate to number of people living in the apartment. More the people, more the water consumption and hence more money to be paid.

I feel it gets more complex when guests stay in an apartment as they should be also charged for water consumption.

Apartment # Persons and Total Days
1 2 persons for 26 days, 1 guest for 5 days
2 4 persons for 31 days, 1 guest for 10 days, 3 persons for 5 days
3 3 persons for 31 days
4 0 persons for 31 days
5 1 persons for 9 days
6 3 persons for 31 days
7 2 persons for 31 days
8 3 persons for 31 days

Hope I have made my problem clear. What kind of easy-to-use mathematical solution can be used for such problem?

Purus
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1 Answers1

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You have to calculate the person hdays. so multiply the number of persons with the number of days the stay. keep the information for all apartments, then add all numbers up and divide the cost by this number this gives you the cost per person and day. now for every apartment you multiply it by its number. your apartment two is not possible you can not have 4 p for 31 days and 3 p for 5 das or are there 7p for 5 days and 4 for 26 days? second problem. at least in my country you have "basic costs" which you have to pay even if no water is consumed. this basic cost should be evenly distributed to the 8 apartments, the rest like above-

trula
  • 1,472
  • It seems quite clear to me: four people stayed all 31 days in the apartment; in addition, one person stayed for 10 days, and three people stayed for 5 days. So the total numbers of person-days is $4\times 31+1\times 10+3\times 5$. – TonyK Aug 02 '22 at 16:40
  • for apartment 2, these are additional guests who have visited and stayed over there. – Purus Aug 02 '22 at 16:42
  • Thanks. solved it. – Purus Aug 02 '22 at 16:48