Expert: Lynn Houston - 3/7/2009

Question
Please help solve this math disagreement between me and my roommate.

The rent where I live now is 1575 total.

Before I moved in the 3 people living here each paid 525 in rent, but when I moved in I took a bedroom for myself and the extra person moved into the living room.  Because he had to live in the living room, the other roommate who has a room and I have agreed to each pay an extra 50 dollars above the original rent in order to drop his rent by 100.

So now, each of us who have a bedroom pay 575 a month, and the guy in the living room pays 425 a month.

The problem is, when I informed him during an argument that I pay 150 more than him each month, he said that can’t be right, his rent would be much lower and we only pay 50 more each month.  I informed him that since he is no longer paying the original rent of 525 but is now paying 425, that I pay 150 more than him, not only 50.

He claims that’s not the right “equation” even though I’ve informed him it’s basic arithmetic and there are no hidden “equations” involved.  He can’t seem to get that by taking one hundred away from his rent, and adding 50 to ours, the DIFFERENCE is greater than just the 100 subtracted from his original rent or the 50 added to ours, and is actually 150.

So please explain to him that when he pays 425 in rent, and the other two roommates pay 575 in rent, both of his roommates pay 150 more than he does each month.  I cannot get him to listen to me, he will only listen to a math expert.


Answer
Of course, as math rules dictate, you are correct.  Try to explain it using a number line.  Mark 525 and in increments of 10 up to 575 and down to 425.  So him that the space between the two rents (575 and 425) is now 150.  If his rent went down 100 and yours went up 50, the difference between the two rents is now 100+50 or $150.