Hi, I'm John and I've been having a disagreement with my roommate about how much rent she pays. If this isn't the right area for this question, let me know and I'll repost elsewhere. This seems pretty basic, but I'm having trouble understanding how to view this. Your help would be appreciated.
I live in a two bedroom house along with two other roommates. Rent for the home is $1575/month. Split three ways equally, rent would *normally* be $525 each/month. Roommate #1 and Roommate #2 each have their own room and I live in the living room. Because of this arrangement, both Roommate #1 and #2 have agreed to pay $50 more a month, their rent is $575. I have a reduced rent of $100 and pay $425. These numbers, $575+$575+$425= $1575.
For the last few days, Roommate #2 has been insisting that she and Roommate #1 pay $150 more than I do, not $50. According to her argument, that would make rent for #1 and #2 $675, my rent staying at $425. But if this was true, our rent would total $1775, right? She continually refutes this by arguing that $575-$425=$150, thus she "pays" $150 more/month.
I feel like either she's lost it or I have. Anyone care to explain why which one of us is wrong and which one of us is right, in explicit, formulaic detail? Or if there are several ways of looking at the situation, could you explain to me why/how my roommates don't pay $50 more a month and I don't pay $100 less in this arrangement?
Thanks so much for reading this,
Your roommates are right- they are NOT paying "$50 a month more than you". They are paying $50 a month more that 1/3 of the total rent but you are not paying that 1/3 yourself.
If they are really to pay $50 a month more than you, let "x" be the amount you pay. Then each of your room mates pays x+ 50, for a total of x+ (x+50)+ (x+ 50)= 3x+ 100. That must equal $1575:
3x+ 100= 1575 so 3x= 1475 and x= 1475/3= 491.67. You should pay $491.67 and each of your room mates should pay 541.67. Because of the rounding off, that adds to 491.67+ 541.67+ 541.67= $1575.01. You can send me the extra penny!