split room fees

Question

I booked a hotel for a total of 7 nights at $1778. 3 people are staying all 7 nights. 2 additional people will be staying only 5 nights. What are the totals for each person?

Answer 1

I think there are 2 reasonable answers:

 

1) The people who staying in the room on a given night should split the cost evenly.  The room goes for $254 per night.

When 5 people are staying, each should pay $254/5 = $50.80.  When 3 people are staying, each should pay $254/3 = $84.66 (plus 2/3 of a penny!).  

Cost for each of the 3 staying 7 nights would be 5·($50.80) + 2·($84.67) = $423.33  (with proper rounding for the final amount)

Cost for each of the 2 staying 5 nights would be 5·($50.80) = $254.00.

The grand total of these assessments is $1777.99. Somebody will need to kick in an extra penny.

 

2) Everybody should pay the same per night they stayed, regardless of how many nights that was.  One person for one night is 1 person-night.  In this scenario there are 31 person-nights.  Each person-night costs $1778/31 ≈ $57.35483871 

Cost for each of the 3 staying 7 nights would be 7·($57.35483871) = $401.48 (with proper rounding)

Cost for each of the 2 staying 5 nights would be 5·($57.35483871) = $286.77 (with proper rounding)

The grand total of these assessments is $1777.98. Each of the 5-nighters could kick in an extra penny.

Answer 2

There may be other ways to look at this, but here is how I would do it.

$1778 for 7 nights equates to $254 per night.

For the first 5 nights, there will be 5 people staying.  This equates to $254/night x 5 nights = $1270 = $254 per person

For the 2 remaining nights, there are only 3 people staying. This equates to $254/night x 2 nights = $508 = $169.33 per person

Thus, those 3 people staying all 7 nights would owe $254 + $169.33 = $423.33 TOTAL

Those 2 staying only 5 nights would each owe $254 TOTAL

 

3 people @ $423.33 each = $1270

2 people @ $254 each = $508

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Total = ..........................$1778