Calculating Rent Payment: 3 roommates in a 3 bedroom house; master bdrm is $100 more

[El Demente]

Hey guys,

We are a total of 3 roommates in a 3 bedroom house. The total rent is: $1600. We have decided that the person in the master bedroom will pay $100.00 extra per month.

I was thinking we take 1600/3+100 and master pays: $633.33. Then we take 1600/3-50 and the other 2 pay $483.33 each.

My roommate says you would take 1600 and subtract 100 for the master bedroom and then divide by 3 and then you add 100 back on for the person paying the master. So (1600-100)/3+100 = $600 for the master, and (1600-100)/3 = $500 for the other 2 bedrooms.


Which one is correct and why?

 

[HallsofIvy]

your room mate is correct. If you each paid 1/3 of $1600 and one person paid an additional $100, then you would pay a total of
3(1600/3)+ 100= 1600+ 100= $1700, $100 too much. Subtracting the $100 first to get $1500, then dividing by 3, two people would be paying 1500/3= $500 and the person occupying the large bedroom would pay 500+ 100= $600. 500+ 500+ 600= $1600.

 

[El Demente]

I think I get it, but the total would not = 1700 if I add the 100 to mine but subtract 50 from each of them though?

 

[Dr.Peterson]

Hey guys,

We are a total of 3 roommates in a 3 bedroom house. The total rent is: $1600. We have decided that the person in the master bedroom will pay $100.00 extra per month.

I was thinking we take 1600/3+100 and master pays: $633.33. Then we take 1600/3-50 and the other 2 pay $483.33 each.

My roommate says you would take 1600 and subtract 100 for the master bedroom and then divide by 3 and then you add 100 back on for the person paying the master. So (1600-100)/3+100 = $600 for the master, and (1600-100)/3 = $500 for the other 2 bedrooms.

Which one is correct and why?

The roommate is correct, but not for the reason Halls gave.

You have two conditions: the total is to be $1600, and the person in the master bedroom is to pay $100 more than the others.

Just check which solution satisfies the conditions:

A: $633.33 + $483.33 + $483.33 = $1599.99, which is effectively $1600; but $633.33 - 483.33 = $150, not $100.

B: $600 + $500 + $500 = $1600; and $600 - $500 = $100.

So only the second method works. That's why it's correct.

If you're asking what was wrong about how you worked out the first answer, it's that you're starting with three equal amounts, and then adding 100 to one while also subtracting 50 from the others. If two people start in the same place, and one moves forward 100 feet while the other steps back 50 feet, they end up 150 feet apart, not just 100.

Your roommate started with equal numbers and only added 100 to one of them, so the resulting difference is 100, as required.

 

[HallsofIvy]

I think I get it, but the total would not = 1700 if I add the 100 to mine but subtract 50 from each of them though?

If you first divide 1600 by 3, you would get $533.33. If you add $100 to yours, that would be $633.33, If you subtract $50 from each of theirs, they would pay $483.33. Yes, 633.33+ 483.33+ 483.33= 1599.99 (and someone will have to pay the additional penny that was lost by rounding) but you are now paying 633.33- 483.33= $150 more, not $100 more, than the other two.

 

[El Demente]

Thank you guys very much!

 

[Steven G]

Hey guys,

We are a total of 3 roommates in a 3 bedroom house. The total rent is: $1600. We have decided that the person in the master bedroom will pay $100.00 extra per month.

I was thinking we take 1600/3+100 and master pays: $633.33. Then we take 1600/3-50 and the other 2 pay $483.33 each.

My roommate says you would take 1600 and subtract 100 for the master bedroom and then divide by 3 and then you add 100 back on for the person paying the master. So (1600-100)/3+100 = $600 for the master, and (1600-100)/3 = $500 for the other 2 bedrooms.


Which one is correct and why?

Your roomate is correct. You all three want to share the rent equally except one person pays $100 more than the others. So imagine if that person each month pays $100 and then the three of you (including the person who paid $100 already) split the rest equally. Now all of you paid exactly the same amount for the 'split equally' part plus one person paid the initial $100.

 

[tkhunny]

I think I get it, but the total would not = 1700 if I add the 100 to mine but subtract 50 from each of them though?

One more, just for fun...

1600/3 + 100 assumes you know what everyone else is paying (1/3), and you don't actually know that.

"P" is the base amount

P + P + (P+100) = 1600

3P + 100 = 1600

3P = 1500

P = 500

You can see the mechanics and the whys and wherefores quite clearly, here.

 

[El Demente]

One more, just for fun...

1600/3 + 100 assumes you know what everyone else is paying (1/3), and you don't actually know that.

"P" is he base amount

P + P + (P+100) = 1600

3P + 100 = 1600

3P = 1500

P = 500

You can see the mechanics and the whys and wherefores quite clearly, here.

Super helpful to get it through my thick skull the correct way to think about it!