What have you tried so far?
I went on holiday with my girlfriend and we both paid for a variety of costs during the trip. Now that we are home, we are having difficulty working out who owes who what...
Before the trip, Girl 2 deposited €1879 into Girl 1's bank account. Girl 1 gave Girl 2 €537.50 of that money so that she would have cash to spend on herself during the trip.
During the trip, Girl 1 paid: €2,222 worth of shared expenses towards the trip. Girl 2 paid: €444 worth of shared expenses towards the trip.
If they want to split all shared expenses - who owes who money and how much?
"During the trip, Girl 1 paid: €2,222 worth of shared expenses towards the trip. Girl 2 paid: €444 worth of shared expenses towards the trip." So there were 2222+ 444= €2666 in total expenses. Half of that is €1333. Girl2 still owes 1333- 444= €887
Girl2 orginally gave Girl1 €1879 but then Girl1 gave back €537.50 so that, in fact, Girl2 has already given Girl1 1879- 537.50= €1341.50.
Can you finish it from there?
Girl 2 put $1879 - $537.50 = $1341.50 in the bank account towards the trip, then added another $444 in cash, which meant Girl 2 put $1785.50 towards the trip in total.
That means a grand total of $4007.50 was spent on the trip, which means to be even, each girl should have paid $2003.75.
That means Girl 2 owes Girl 1 $218.25
Another way to look at it is that girl 1 spent $2222 of her own money, and girl 2 spent $444 of her own money. This split evenly means that each girl owes $1333, meaning girl 2 owes girl 1 $1333 - $444 = $889. But remember that girl 2 gave girl 1 $1879 - $537.50 = $1341.50 at the begginning of the trip, which was never touched (remember, girl 1 spent her own money), meaning girl 1 still owes girl 2 back that money. $889 - $1341.50 = $-452.50.
Basically the way I'm looking at it, is whatever of the $1341.50 that girl 1 didn't spend on shared expenses, she owes back to girl 2. In fact if you argue that girl 1 spent an arbitrary amount of the money girl 2 gave her (plus enough of her own money to total $2222), and owes the remainder back to girl 2, then I believe you'll come out to the same value. I'm fairly sure this could be easily argued algebraicly but I don't think that's really needed here.
So girl 1 owes girl 2 $452.5. This is just $2 off from what the original poster said, and I think there was just a little subtraction error in either my post or hallofivy's post. Hallofivy's method looks like the right one to me, I'm just trying to provide another way of looking at that method.
Only at a Math forum can people make such a mess of splitting expenses for a holiday. xD
The subtraction error in HallofIvy's post lies in 1333- 444= €887 (This should be 889)
I did the math too and to me it seems that TheGreenLaser is correct and girl 1 owes girl 2 $452.5
I have calculated it like this
+ = Money gained
- = Money lost
Total spent of 1785.80
Total spent of 880.50
Which means that Girl 2 Owes Girl 1 exactly
This is when all expenses are split directly down the middle and individual spending money is also split. If this is not how you wished for it to be calculated you need to be more precise about your description.