Conference rusure::math

698.0. "Rent division problem" by SEMI::NG () Tue May 05 1987 10:34

    I'm not sure this is the place. It's kind of a trivial everyday
    life problem:
    
    I am living in a apartment with 3 other persons. The rent is $900/month.
    However, one of the 4 persons just move in in the middle of last
    month (4/13). The problem is calculating how much each of us should pay.
    
    Let's call the fourth person D and the other A,B, & C.
    
    Proposed method 1:
    	Persons A, B & C have lived in the house for the whole month,
    i.e. 30 days, and person D has lived in the house for 18 days.
    So person A, B & C each will pay:
    
    				30/(18+3*30) * 900 = 250
    and person D will pay:
    
    				18/(18+3*30) * 900 = 150
    
    Proposed method 2:
    	The rent is $900/month, i.e. $30/day.
    In the first 12 days of the month, only person A, B & C lived in
    the house. So, for the 12 days, each of A, B & C should pay
    	30/3 = $10 per day.
    For the next 18 days, all 4 persons lived in the house; so each
    of us should pay 30/4 = $7.50 per day.
    
    Hence, person A, B & C each should pay:
    				10*12 + 7.50*18 = 255
    and person D will pay:
    					7.50*18 = 135
    
    What I don't understand is that these 2 methods look the same, (both
    seem to be right,) but the results are different.
    
    Could someone tell me what went wrong? Which one is right?
    Maybe both are wrong.
    
    Thanks.
    
    david
    

Nothing wrong; method 1 prorates the rent per tenant-day, method 2 per day.
Since your landlord most likely rents by the month, not by the person-month,
method 2 seems the fairest pass-thru; also, the fourth sharer didn't impact
the crowding until s/he actually arrived, right?

    How would you solve this if the person lived there for eight months out
    of twelve?  You would not make them pay a portion of the four months
    they were not there, would you?  Each month they are there, divide up
    the rent.  So, each day they are there, divide up the rent.
    
    
    				-- edp