How to balance an expense sheet with different percentages

mathetes Thank you for sharing this! I guess the question I have boiled into one sentence is:

Is there a function or formula that I can use to balance an expense sheet with repayments from 2 sources. 

I was not able to find an equation that did this in the shared spreadsheet. I currently use the following functions:

Value 1: =SUMIFS(tblTransactions[Amount],tblTransactions[Person],'Data Validation'!E2,tblTransactions[Category Type],'Data Validation'!C2)*-1 [I use this function to sum the total expenses per person then multiply by -1 to return a positive value]

then

=SUMIF(tblTransactions[Category Type],"Expense",tblTransactions[Amount])*-1 [I use this function to sum the total expenses between both people in the table, then multiply by -1 to return a positive value]

then

Value 2: I multiply the the value returned above by .55 for person 1 and .45 for person 2 to return the value each person is responsible for]

then

Value 3: =SUMIFS(tblTransactions[Amount],tblTransactions[Person],'Data Validation'!E2,tblTransactions[Category Type],'Data Validation'!C10) [I do this to sum the total payments made by person 1 to the other to balance the expense sheet]

then

I subtract Value 1-Value 2-Value 3

This only works if person 1 pays person 2. When person 2 pays person one the logic fails.

Any guidance would be greatly appreciated!