How to divide 276 with 15 people?

Question

I have a math question. In our bachelor room our water bill is 276. It is a bill for 31 days. But out of this 15 people, only 12 people used water for 31 days. one went for vacation after 20 days that means he drank only 20 days. another drank only 25 days and third one drank only 26 days. In this case how to divide the bill equal to what they drank. I need the answer to be applied in excel so no a+b=x type answer. Only addition, divide and multiplication, can you find the answer please

*How I did it is: 276/31/15=0.59 *So full time 12 people’s share= 12X0.59X31=219.48 *20 day guy’s share=11.87 *25 day guy’s share=14.84 *26 day guy’s share=15.43

*So the total is 261.62 *Difference is 14.38 *My question, should I divide this 14.38 with all 15 friends or 12 friends only

Answer 1

If we denote the cost of one unit of water by $x$ (where cost of one unit of water is the cost of drinking water by one person by one day), we have: $$(20+25+26+12\cdot 31) x = 276$$ Thus $$x=\frac{276}{443}$$ So if one person had been drinking water by $k$ days, he'll pay for it $$k\cdot \frac{276}{443}$$

Answer 2

Let us say: the $12$ full time people each pay $A$.

Fairness suggests that a person who stayed $N$ days should pay $\frac N{31}\times A$. Thus we have $$276= 12A +\frac {20}{31}\times A +\frac {25}{31}\times A +\frac {26}{31}\times A \approx 14.29\times A$$

This implies that $\boxed {A = 19.314}$