SOLUTION: 6 people are going on vacation. The total for the cabin rental is $885.40. 4 of the six people are staying for 7 nights while the other 2 are staying for 6 nights. To be fair to

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: 6 people are going on vacation. The total for the cabin rental is $885.40. 4 of the six people are staying for 7 nights while the other 2 are staying for 6 nights. To be fair to       Log On

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Question 102540: 6 people are going on vacation. The total for the cabin rental is $885.40.
4 of the six people are staying for 7 nights while the other 2 are staying for 6 nights. To be fair to everyone I need to know how much the 4 owe for 7 nights and the 2 owe for 6 nights. It seems simple, but for the life of me I can't figure it out. Your help with this would be greatly appreciated.
Answer by doukungfoo(195) About Me  (Show Source):
You can put this solution on YOUR website!
Well if the cost of the cabin rental for 7 nights is $885.40
Then the cost per night would be
885.40/7 = 126.4857143
now for the first six nights this cost per night is being split 6 ways so
126.4857143/6 = 21.08095238
So for the first six nights everyone chips in aprox. $21.08 each night.
Now the last night there are only 4 people to split the cost.
The cost is still the same 126.4857143 per night that we already figured, but this time there are only 4 people so the cost per person for the last night is
126.4857143/4 = 31.62142858
So for the last night the remaining 4 people each chip in aprox. $31.62

Ok lets see what we've got the total cost for each person staying 7 nights is
$158.11
And the total cost for the two people only staying 6 nights is
$126.48
Lets check this against the known total cost of the room.
If 4 people each chip in $158.11 thats 4*158.11 = $632.44
and 2 people each chip in $126.48 thats 2*126.48 = $252.96
632.44 + 252.96 = $885.40