Excel/Google Sheets Solver Difficulty

[DumbEngineer]

I am trying to figure out which elements of a set of numbers (amounts) total to a target value. I am creating a google sheet to keep track of what my roommates pay me, where I receive both full and partial payments of bills from my roommates but documentation indicating what bills are being paid is lacking. The spreadsheet below is similar to what I am doing. In the Bill Owed column, I want to format the cells so that it tells me which bills still need to be paid. For example, for Roommate A the Bills Owed Column should display "Cable, Water, Electric, & $250". For Roommate B it should say "None". For Roommate C is should say "Water, Electric, Rent". For Roommate D is should say "Cable, Water, Rent". Roommate F would still owe "Water, Rent". I think I might be able to use the solver command; however, I'm not quite sure how to use it. I also think it might run into a problem with Roommate A where they only paid $100 and not any bill in particular. How do I fix this and is there a way this spreadsheet could be more efficient? I don't want to use a bunch of nested IF statements.

Thanks

Bills			Per Person
Rent	2200
Cable	127.85		21.31
Water	108.30		18.05
Electric House	273.72
Electric Garage	8.59
Electric Total	282.31		47.05
Grand Total	2718.46		86.41
Roommates	Rent	Utilities	Amount Owed	Amount Paid	Amount Still Owed	Bill Owed
Roommate A	350	86.41	436.41	100	336.41
Roommate B	330	86.41	416.41	416.41	0
Roommate C	400	86.41	486.41	21.31	465.1
Roommate D	420	86.41	506.41	47.05	459.36
Roommate E	370	86.41	456.41	21.31	435.1
Roommate F	330	86.41	416.41	68.36	348.05
Total	2200	518.46	2718.46

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