I need to rent a house and split the cost between 7 people - but not
equally. The cost of the house is $957.00 for three nights. Three of
the seven people will be staying in the house for three nights.  Four
of the seven people will be staying in the house for only two nights.
So, the three people staying for three nights should pay more than the
four people who are staying only two nights.  My question is... how
much money should the people staying for three nights pay and how much
should the people staying for four nights pay? In addition to the
total cost for each person, I need an explanation of the way you
computed it so I can explain it to my friends so they will believe me.

Thanks.

---

Request for Question Clarification by sublime1-ga on 05 Apr 2006 17:52 PDT

"Three of the seven people will be staying in the house for
 three nights.  Four of the seven people will be staying in
 the house for only two nights."

[...]

"...how much should the people staying for four nights pay?"

Does not compute.

---

Clarification of Question by johnsoda24-ga on 07 Apr 2006 12:42 PDT

just to clarify, i mean to say "how much should the three people
staying for three nights pay and how much should the four people
staying for two nights pay"?

does that help?

Hi johnsoda24,

I believe rracecarr-ga has got the right idea. Look at it this way:

People     Night 1     Night 2     Night 3
1            X           X           X 
2            X           X           X 
3            X           X           X 
4            X           X                 
5            X           X                
6            X           X                
7            X           X         

Three people (numbers 1, 2 and the 3 in the diagram) are staying 3
nights. Four people (numbers 4, 5, 6 and 7) are staying 2 nights.

Since there are 17 people-nights (count the X's), each person would
pay 957/17 which equals to approximately $56.29 per night.

Therefore the 3 people staying 3 nights would pay 56.29x3=$168.87 each.
And the 4 people staying only 2 nights would pay 56.29x2=$112.58 each.

To check the math:
168.87x3=$506.61
112.58x4=$450.32
506.61+450.32=$956.93. I'm sure one person would be willing to pay the
difference of 7 cents. :-)


I hope this explanation is helpful. If you have any questions
regarding my answer please don't hesitate to ask before rating.

Best regards,
Rainbow

957 over 3 nights is 319 per night.  
On nights 1 and 2, each person pays 319/7 = 45.57
On night 3, the 3 people who stay pay 319/3 = 106.33

Therefore the 4 people who stay 2 nights pay 91.14
The 3 people who stay 3 nights pay 197.47. As a sanity check that is:
4(91.17) + 3(197.47) = 957

Or, since there are 17 people-nights, each person could pay 957/17, or
about $56.29, for each night they stay.  That would be $112.59 for the
2-nighters and $168.88 for the 3-nighters.

I was just going to post the same people-night suggestion but rracecar
beat me to it.

However, I would like to add that this solution has the property that
everyone pays the same price per night.  That is, the people who stay
3 nights pay 1 and a half times what the two night people pay.

Although I guess you could argue that the house is worth more when
there are less people in it, because it is less crowded and you get a
bigger share of the common areas.  But it probably isn't worth over
twice as much.

And you thought this was a simple problem.

I wanna know how the people staying four nights in a house rented for
three nights are gonna their bit.

racecar, can you explain how you came up with 17 people-nights? 7
people X 3 nights = 21.  I guess I don't understand? Also, do you
agree with frankcorrao-ga's answer?

Thanks.

thanks everyone for your comments.  if someone could give me a
definitive answer i would really appreciate it. i can't decide which
calculation is correct.

Thanks again.

Johnsoda,  
Why wasn't that a five star answer?  Sometimes here, one gets the
impression that there are people who are bothered by the fact that the
answer to their question was something they could have figured out
themselves and downgrade a perfect answer, perhaps on the principle: 
"Geez, I could have figured that out.  If it is that simple, the
answer isn't worth five stars."
I don't know if that was your thought, but a correct and complete
answer deserves five stars.

Myoarin     Have a good time, wherever.