OK basic story is that my cousin is a tightarse, so i want to get the correct figure with explanation so i can make sure he pays the right amount for a holiday apartment we are sharing. :mrgreen: Ive been trying to work this out, for some reason, it seems so simple, however it just doesnt work :? Now i dont really care as its not a great deal of money or anything, im just confused why i cant work it out. and it's a point of principal.
Ok so The Holiday apartment will cost $750 for one week (7 days). 5 people will be going in total. 2 of them are staying for only 3 days. the remaining three will be there for the full week. How much do the 2 people need to pay for the 3 days they are there? Please explain it as i'm just baffled why i cant work it out.
The results im getting are either that the total amount falls short of the $750 needed, or in percentage form they aren't paying the correct amount for the proportion of time they are there for.
This has just turned into one of those got to know things as its annoying me i cant work it out

Way of topic for this forum, just thought id throw it up too see what you guys can do :lol:

Quote from Rotatox :

OK basic story is that my cousin is a tightarse, so i want to get the correct figure with explanation so i can make sure he pays the right amount for a holiday apartment we are sharing. :mrgreen: Ive been trying to work this out, for some reason, it seems so simple, however it just doesnt work :? Now i dont really care as its not a great deal of money or anything, im just confused why i cant work it out. and it's a point of principal.
Ok so The Holiday apartment will cost $750 for one week (7 days). 5 people will be going in total. 2 of them are staying for only 3 days. the remaining three will be there for the full week. How much do the 2 people need to pay for the 3 days they are there? Please explain it as i'm just baffled why i cant work it out.
The results im getting are either that the total amount falls short of the $750 needed, or in percentage form they aren't paying the correct amount for the proportion of time they are there for.
This has just turned into one of those got to know things as its annoying me i cant work it out

Way of topic for this forum, just thought id throw it up too see what you guys can do :lol:

So it costs $750 for the week, and 5 people are staying for the week - thats 35. 2 people are staying for 3 days - that's 6. 35+6=41 Divide 750 by 41, and that's the cost per day, per person - $18.29. The people who are staying 3 days pay $54.87 each, the people who are staying the week pay $128.03 each.

Quote from J@tko :

So it costs $750 for the week, and 5 people are staying for the week - thats 35. 2 people are staying for 3 days - that's 6. 35+6=41 Divide 750 by 41, and that's the cost per day, per person - $18.29. The people who are staying 3 days pay $54.87 each, the people who are staying the week pay $128.03 each.

Sorry Jack...your calcs went wrong when you worked out the splits. I can see what you were to trying to get at, but you have added the "6" to the "35"....whereas it IS ALREADY INCLUDED!!!!

1 week = $750
each person will pay 750/5 for whole week
this equals 150 per person for 7 nights.
cost per person per night is 150/7
cost for your 2 friends that stay 3 days= ((150/7)*3)
Equals as close as damn it $64.30 each

Quote from Bladerunner :

Sorry Jack...your calcs went wrong when you worked out the splits. I can see what you were to trying to get at, but you have added the "6" to the "35"....whereas it IS ALREADY INCLUDED!!!!

Yes - thanks for spotting my error - I didn't read it properly!

Quote from Rotatox :

OK basic story is that my cousin is a tightarse, so i want to get the correct figure with explanation so i can make sure he pays the right amount for a holiday apartment we are sharing. :mrgreen: Ive been trying to work this out, for some reason, it seems so simple, however it just doesnt work :? Now i dont really care as its not a great deal of money or anything, im just confused why i cant work it out. and it's a point of principal.
Ok so The Holiday apartment will cost $750 for one week (7 days). 5 people will be going in total. 2 of them are staying for only 3 days. the remaining three will be there for the full week. How much do the 2 people need to pay for the 3 days they are there? Please explain it as i'm just baffled why i cant work it out.
The results im getting are either that the total amount falls short of the $750 needed, or in percentage form they aren't paying the correct amount for the proportion of time they are there for.
This has just turned into one of those got to know things as its annoying me i cant work it out

Way of topic for this forum, just thought id throw it up too see what you guys can do :lol:

My interpretation attached in zip file (small .xls file within)

In short - 3 day people pay $64.29, 7 day people pay $207.14.

But there are several ways to skin a cat, just as there are multiple ways of splitting the cost up here

thankyou, however im confused. The remaining 3 people need to pay $207.3 each for the whole week

How come the 2 people pay 64.3 each when they are there for almost the time? Each of the remaining people are paying over 3 times what they are paying yet they are staying just over double the time

I just said that for 3 days the daily cost (750/7) is divided by 5 people, and for the remaining days the daily cost is divided by 3. Therefore the people who are only staying 3 days pay considerably less, as there time is split between 5 people. That's how I would do it, as I wouldn't want to be paying for the other 3's time there when I wasn't.

Days 1, 2 and 3
Each person pays 750/(5*7) = 21.43 each

Days 4, 5, 6, 7
Each person pays 750/(3*7) = 35.71 each

Three day people = 21.43 * 3
Seven day people = [21.43 * 3] + [35.71 * 4]

Yeah i guess the difference with me is that im the type of person if i saw that figure, would think that doesnt seem right, and would offer more, i just know my cousin doesnt have that mentality so want to know the exact figure.

Assuming that the total price is charged over 7 days (usually accommodation is charged by nights):

For the two days you have 5 ppl
750 / 7 = 107 ($107 per day in total)
107 / 5 = 21.5 (each of the 5 ppl pay $21.5/day for 3 days)
21.5 * 2 * 3 = 128.5 (the 2 ppl will pay $21.5 for 3 days, $128.5)

Totals so far
21.5 * 5 * 3 = 322.5 (amount paid in total by all)
750 - 322.5 = 427.5 (amount left to be paid by 3 ppl over 4 days)

For the remaining time
427.5 / 4 = 106.88 (paid per day)
106.88 / 3 = 35.63 (per person)

-----

Amount paid by each of the two who leave early is 128.5 / 2 = $64.25
Amount paid by each those who stay the full duration is 64.25 + 35.63 * 4 = $206.77

NB: Numbers are rounded up, accommodation is usually charged per night.

3-days:

750*(3/7)/5 = 64,29 per person

7-day stayers:

[750*(4/7)/3]+[750*(3/7)/5]= 207,14 per person


I hope it looks overly complicated, but in short, I got the same results than Tristan. :P

why is the daily rate intially counted for 5 people?

What if 3 people were going to stay for a full week. And the 2 others asked to stay for 3 days after we had booked and worked out our daily rate (3ppl)? see why im confused??

Quote :

why is the daily rate intially counted for 5 people?

Because you said 5 ppl booked for a week.

Quote :

What if 3 people were going to stay for a full week.

Then the initial rate would be calculated for 3 ppl

Quote :

And the 2 others asked to stay for 3 days after we had booked and worked out our daily rate

In which case you'd have 5 ppl. When there are 5 ppl everyone pays as if 5 ppl booked, when there are 3 ppl everyone pays as if 3 ppl booked.

Realistically what you'd do is have the 3 ppl pay as intended, then work out the amount that the 2 others should pay and they pay you back. That's assuming the price of the booking does not relate to the amount of ppl staying in the accommodation.

Now I'm confused too. What are you trying to say?

for another spin on it does the place your staying have a more expensive daily rate over the weekly rate?

If so you could charge the two that stayed for three days only the "daily rate"/"five people" x "two people" per day that would be fair also

I hope people are starting to understand why im confused!

Lets say 3 people booked and paid, then 2 people asked to come....how much do they owe us for the proportioned time they are there?

The same amount ($64.30) as you've already been told they'll pay. If they'd pay at the 3 person rate they'd be overpaying, hence the 5 person rate when there are 5 ppl.

I did it this way:

3 people staying 7 days = 21 people days
2 people staying 3 days = 6 people days
TOTAL = 27 people days

$750/27 = $27.78 per person per day

So the two people staying three days pay $27.78*3 = $83.33 each.
The three people staying seven days pay $27.78*7 = $194.44 each.

I'll leave you to argue over the remaining $0.02

Each of the 3 people should be paying $250 (750/3).

But as two people are popping in for 3 days you can either

1. Make up a suitable number you are all happy with

2. Assume they pay 3/5 of the daily cost (as they are there for 3 days) each, which is 64.29, they have to pay each of the other three people $21.43 each.

Quote from StewartFisher :

I did it this way:

3 people staying 7 days = 21 people days
2 people staying 3 days = 6 people days
TOTAL = 27 people days

$750/27 = $27.78 per person per day

So the two people staying three days pay $27.78*3 = $83.33 each.
The three people staying seven days pay $27.78*7 = $194.44 each.

I'll leave you to argue over the remaining $0.02

Thats the figure i was trying to arrive to!....doesnt that seem the fair way in regards to time spent in the apartment ?

Obviously you are one of the original three, and want to get the other 2 to pay as much as possible to reduce your costs...

Either way is fair, it's up to you. And even better way, if they are your friends, is to ignore science and maths, and talk to them.

From a business point of view the two that stay for only 3 days should be paying at a higher rate than the rest as they are not staying for the entire week they are not eligible for the "weekly rate"

You purchased the holiday appartment rental at a bulk rate so the three that stay for the entire week should get the benifit of that rate.

This means that the two that stay for three days should pay the equivelent of their share of a daily rate rental.

Lets say the daily rate is $120/day and the weekly rate is $750/week.

This would mean that the two that stay for 3 days would pay 120/5 which is $24 per person per day or $72 each for the three days. The remainder would pay (750-144)/3 which is $202 each for the week.

This would be the fairest way imo

yeah see how many results i got...what im saying is (again :schwitz is the daily rate is a fixed figure you would say.....why should it change when certain people are not there. It should be the same for everyone per day multiplied by how many days you are there in equal amounts.

Quote from Glenn67 :

This would mean that the two that stay for 3 days would pay 120/5 which is $24 per person per day or $72 each for the three days. The remainder would pay (750-144)/3 which is $202 each for the week.

This would be the fairest way imo

So the three people who stay the extra 4 days should pay almost three times as much as the people who left after 3 days? Doesn't sound very fair to me.

i just a go at it, and i would do it exactly the same way StewartFisher didi it :
calculate a cost per day and person (2 people for 3 days = 6 people days and 3 people for 7 days = 21 peopledays, so a total of 27 peopledays = 750 / 27 = 27,77 per people and day, so each people that stayed for 7 days has to pay 83,31 and everyone who spent 7 days has to pay 194,39)

yeah im pretty sure that is the correct way too, the problem is the initial daily rate calculation, 5 people or 3 people. It needs to be met in the middle. That way the daily rate is constant for the whole week which is the way it should work. Its a daily rate after all
If we change it to have teh daily rate calculated with 3 people and charge the other people that rate it ends up being more than $750 so that isnt fair. Stewartfishers way is fair and equals everything out.

My cousin is an ok bloke,just tries to get out on the cheap usually if he can manage it

Thanks to everyone who helped...hopefully this holiday turns out to be an enjoyable one lol.