1. ## Mathematical Conceptual Problem

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, John 2. Originally Posted by notamathwhiz 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,

John
Well the thing is it's not as simple as 'they're paying $50 more than you'. Firstly anything extra they pay is removed from your rent, so if they pay$50 more then you pay $50 less and the actual difference is$100. Also, there's two of them so any increase in what they may is doubly matched a decrease in your payment. The fact is, they each do pay $150 more per month than you. 3. 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!

4. ## I have an apology to make!

Thanks so much. I've been on a few other forums and up until now I haven't understood the situation. I appreciate you explaining it to me in algebraic form, it's much easier to grasp!

John