Consolidating Debts for Bills

I'm having difficulty figuring out exactly how I can look up how to go about developing a spreadsheet that sums up the scenario below. I'm just so rusty that I feel like the answer is simple, but I keep ending up with results that won't work if the numbers were to be switched around and negative numbers get involved; it just becomes a mess. Feel free to just point me towards a link that will help me answer this question myself if this is pretty much a waste of other people's time.

PERSON-A owes PERSON-J $30.00
PERSON-J owes PERSON-A $51.50
PERSON-N owes PERSON-A $51.50
PERSON-N owes PERSON-J $87.95

What I'd like to have setup is a formula that consolidates debts for different expenses. Here's what I'm trying to show:

Since PERSON-J owes PERSON-A $51.50 and PERSON-A owes PERSON J $30, PERSON-J really only needs to give PERSON-A $21.50.

PERSON-N owes PERSON-A $51.50 and owes PERSON-J $87.95, but since PERSON-J owes PERSON-A $21.50, I would like the spreadsheet to show that PERSON-N should pay PERSON-A $73.00 ($51.50+$21.50) and pay PERSON-J $66.45 ($87.95-$21.50); thus eliminating the need for PERSON-J to give PERSON-A any money.

Thanks for the quick response. I got a half-finished version that works for now and should give a general idea of what I'm trying to do, but the problem occurs when I enter a dollar amount larger than $315 into E3, when E10 has $220 in the cell. It results in E24 having a negative number which shouldn't be happening as it would no longer make sense with what I'm trying to do. Please advise if I'm still not being clear....when i think too much about it it only gets more confusing for me.

https://spreadsheets.google.com/ccc?...thkey=CLrQqPcI