OT: help me do math

[seanile]

i remember an interesting thread from a while back in which there was a math question that could be solved a few different ways, but only one was right. i've got a real world example that i'd like some input on. also, please excuse the absurdity of some of these numbers and the living situation...welcome to boston real estate.

i'm signing onto a one year apartment lease with 5 other individuals, 6 total.

in order to sign the lease, the following was paid:
a) first month's rent.
b) last month's rent.
c) security deposit equal to a month of rent.
d) realty broker's fee.

the monthly rent is 5650 total for the 6 of us. the fee was 5500.

four tenants signed the lease originally, and i'm one of two after-the-fact add-ons that needs to reimburse each of those four individually. edit: the 6th tenant (me being #5) is yet to be gotten.

the question:
if each of them paid one of the respective responsibilities (a through d) how much do i owe each of them?


my math was as follows:
5500/6=916.66 for the fee
(5650*3)/6=2825 for the other three, 941.66 respectively.
my total outlay=3741.66
note: 3741.66 is also 1/6th of the grand total outlay (5500+5650*3), 22450.

the following is how the one who paid the broker's fee did the math:
5500-3741.66=1758.34/two remaining rooms=879.17 per room for the fee.
5650-3741.66=1908.34/2=954.17 per room for the other stuff.
954.17*3+879.17=3741.68, my total outlay.

effectively, the same total outlay for me, 3741.66, but with different payment chunks to the respective recipients. i don't quite care what i pay them, because it's the same, but the math of this is bothering me.
funnily enough, the one i wanted to pay $916.66 to asserts that he is only owed $879.17.

i also checked my math by doing:
5500/22450=24.498%...ans*3741.66=916.66
(5650*3)/22450=75.501%...ans*3741.66=2824.99496...ans/3=941.66.

:confused:halp?

[VTCaraco]

I'd advocate for approaching this a different way.

Total cost = $22,450

If equally shared by 6, that makes it $3741.67 per person, right?

First 4 paid as follows:
Person 1 ~ $5650
Person 2 ~ $5650
Person 3 ~ $5650
Person 4 ~ $5500

For their shares to be equal to the $3741.67, they need to be reimbursed the following amounts:
Person 1 ~ $5650 - $3741.67 = $1908.33
Person 2 ~ $5650 - $3741.67 = $1908.33
Person 3 ~ $5650 - $3741.67 = $1908.33
Person 4 ~ $5500 - $3741.67 = $1758.33

Your share, if I'm understanding you correctly, is 1/2 of that.

So you owe each the following amounts:
Person 1 ~ $954.17
Person 2 ~ $954.17
Person 3 ~ $954.17
Person 4 ~ $879.17

Your total outlay is $3741.68 (the 1/6 is rounding)
If #5 does the same, then everyone is square.

[seanile]

see now, you did it the way he did it, which is not how i did it.
very interesting.
anyone else?

edit: are you my housemate?

[Mark McM]

There seems to be some information missing.

The one who paid the broker's fee seems to be assigning some meaning to the number of rooms. What's the connection between number of rooms and payment?

You say that there are 5 other people, but only 4 have made payments - what is the agreement for the amount owed by the 1 out of the 5 who did not yet make a payment? And of the 4 who made payments, 1 paid a different amount - is the plan that in the end, everyone pay equal amounts?

[seanile]

There seems to be some information missing.

The one who paid the broker's fee seems to be assigning some meaning to the number of rooms. What's the connection between number of rooms and payment?

You say that there are 5 other people, but only 4 have made payments - what is the agreement for the amount owed by the 1 out of the 5 who did not yet make a payment? And of the 4 who made payments, 1 paid a different amount - is the plan that in the end, everyone pay equal amounts?

6 people total. 6 rooms total. monthly rent is being divvied up equally per person.
4 people found the place and paid for everything without having the 2 other tenants yet.
i am one of the 2 remaining tenants. the 6th tenant is yet to be gotten.
i am to reimburse those 4 that paid for 1/6th of their portions paid.
3 of them each paid 5650.
1 of them paid 5500.
there is a disconnect between how much each is owed for their respective portion by me.

[VTCaraco]

:confused:halp?

The difference in calculations is based on the fact that the core-4 didn't all pay equal amounts. So the reimbursement for all 6 to be even is changed. In other words, you need to give MORE than 1/6 to the folks that paid the higher amounts and LESS to the person that paid the lesser amount.

Specifically, $12.50 more than 1/6 for each of the first 3 and $37.50 less for the one who paid the broker fee. This accounts for the $150 difference (4 • $37.50) in the core-4's initial payment).

[Mark McM]

This looks like a good time to bring up the missing dollar riddle (https://en.wikipedia.org/wiki/Missing_dollar_riddle), which involves a bellhop trying to evenly reimburse 3 guests for a hotel room fee overpayment

Three people check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 as a tip for himself. Each guest got $1 back, so now each guest only paid $9, bringing the total paid to $27. The bellhop has $2. And $27 + $2 = $29 so, if the guests originally handed over $30, what happened to the remaining $1?

[seanile]

The difference in calculations is based on the fact that the core-4 didn't all pay equal amounts. So the reimbursement for all 6 to be even is changed. In other words, you need to give MORE than 1/6 to the folks that paid the higher amounts and LESS to the person that paid the lesser amount.

Specifically, $12.50 more than 1/6 for each of the first 3 and $37.50 less for the one who paid the broker fee. This accounts for the $150 difference (4 • $37.50) in the core-4's initial payment).

i would've thought that the following was an unbiased way to approach the inequality of the payments though..it accounts for the slight $150 difference between the four given it's not exactly 25% or 75%:
i also checked my math by doing:
5500/22450=24.498%...ans*3741.66=916.66
(5650*3)/22450=75.501%...ans*3741.66=2824.99496...ans/3=941.66.

[VTCaraco]

Simply divide your total costs by 5.
Then each person is responsible for $4,490.

Reimbursements would then be as follows:
Person 1, 2, and 3 ~ $1,160
Person 4 ~ $1,010

Your total cost would be the $4,490 and that's what each person would be in it for.

When you find lucky number 6, that person owe's each of you the exact same amount, $748.33.

$4,490 - $748.33 = $3741.67, the "correct" per person distribution of the initial $22,450.

If you want to make sense of it in another way, $748.33 is 1/5 of the effective per-person of $3,741.67.

[VTCaraco]

This looks like a good time to bring up the missing dollar riddle (https://en.wikipedia.org/wiki/Missing_dollar_riddle), which involves a bellhop trying to evenly reimburse 3 guests for a hotel room fee overpayment

$27 - 2 = $25

Patrons paid $9 per for a total amount GIVEN to the bellhop of $27.
Bellhop pays the $25 and keeps the extra $2.


As for math puzzles, the question of "where did the missing square come from" is better:
https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcQmY1P0TYNFHm85IHtI7v3V6UIBdp29G oTg95YAnFCx1AfFzVgV2g

[Mark McM]

$27 - 2 = $25

Patrons paid $9 per for a total amount GIVEN to the bellhop of $27.
Bellhop pays the $25 and keeps the extra $2.


As for math puzzles, the question of "where did the missing square come from" is better:
https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcQmY1P0TYNFHm85IHtI7v3V6UIBdp29G oTg95YAnFCx1AfFzVgV2g

The "missing" square came from the fact that the two total outlines "A" and "B" aren't the same shape. The red triangle has a slightly shallower slope than the blue triangle. When stacked into shape "A", the combined top surface bends inward slightly. When stacked into shape "B", the combined surface bends outward slightly, filling up a slightly larger total area. Filling up the slightly larger total area with the same pieces creates a void (the "empty" square).

[pncguy]

The "missing" square came from the fact that the two total outlines "A" and "B" aren't the same shape. The red triangle has a slightly shallower slope than the blue triangle. When stacked into shape "A", the combined top surface bends inward slightly. When stacked into shape "B", the combined surface bends outward slightly, filling up a slightly larger total area. Filling up the slightly larger total area with the same pieces creates a void (the "empty" square).

Wow. That's awesome. I am educated in these things and I started with the assumption that the shapes ARE equal. So I couldn't figure it out. Shows you what happens when you start with false assumptions. :eek:

[tourmalet]

A roommate that is added to a lease is not obligated to retroactively cover part of the broker's fee. You only owe for first month's rent (payable to the landlord) and security deposit and last month's rent (payable to the original roommates).

Your outlay will be:

First month's rent to the landlord: $5650/6 = $941.67
Security deposit and last month's rent to roommates: $5650/6 + $5650/6 = $1883.33
Total: $2825.00

When you leave the house, you are entitled to 1/6 of the security deposit or the amount returned by the landlord.

Of course, your roommates can demand that you pay part of the broker's fee, but, having lived in Boston for the last 8 years, I can assure you that it is not customary.

[seanile]

A roommate that is added to a lease is not obligated to retroactively cover part of the broker's fee. they're moving into the house at the same time i am (9/1). had they already been residents, i would agree because the fee would have already been paid in-full and proportionally by the original tenants.
interestingly, somerville caps the signees of a lease at 4, so i won't even be on the lease. i'll just be writing checks.

[tourmalet]

they're moving into the house at the same time i am (9/1). had they already been residents, i would agree because the fee would have already been paid in-full and proportionally by the original tenants.
interestingly, somerville caps the signees of a lease at 4, so i won't even be on the lease. i'll just be writing checks.

This makes waaay more sense. In this case, I agree that your original math checks out.

[Ken Robb]

they're moving into the house at the same time i am (9/1). had they already been residents, i would agree because the fee would have already been paid in-full and proportionally by the original tenants.
interestingly, somerville caps the signees of a lease at 4, so i won't even be on the lease. i'll just be writing checks.

This is probably good news for you because in California and probably most states all signers on a lease are responsibly jointly and severally for the full amount. This means if some of the tennants stop paying the remaining signers are responsible for the whole amount. OTOH a person who doesn't sign probably has no rights other than those granted him by the signers. If they decide they want you to get out you probably have little recourse.

Keeping 6 people happy in one rental may be a challenge. :-)

[seanile]

This is probably good news for you because in California and probably most states all signers on a lease are responsibly jointly and severally for the full amount. This means if some of the tennants stop paying the remaining signers are responsible for the whole amount. OTOH a person who doesn't sign probably has no rights other than those granted him by the signers. If they decide they want you to get out you probably have little recourse.

Keeping 6 people happy in one rental may be a challenge. :-)

that's the way i understand it. and i agree it's preferable, because those four are the ones that know each other..i'm a tagalong.
and i'm kind of interested in moving out of state sooner than later, so if i could set up a sublet and abandon ship without legal liability i'm happy.
i assume you deal with contracts a bit if you're dropping "jointly and severally" in proper form?

[Bob Ross]

i'm signing onto a one year apartment lease with 5 other individuals, 6 total.

I stopped reading there. DON'T DO IT!!!! You'll thank me later.





...just kidding. Sorry, I don't do math.




interestingly, somerville caps the signees of a lease at 4, so ...


Whoa, wait, time out, this is in Somerville MA?!?! DON'T DO IT!!!! You'll thank me later.


:banana:

[seanile]

DON'T DO IT!!!! You'll thank me later.

...

DON'T DO IT!!!! You'll thank me later.
ooohhhh trust me sir!
i'm not so terribly pleased about it, but there are other controlling factors that are making me hustle and stay in somerville, ma.
i'm telling myself that this will all be an exercise in patience and motivation to get outside more often and for longer :D
3 of the housemates are a few years younger than myself as well, so i'm treating it like training for dealing with my brother's incoming niece this fall:eek:

[cnighbor1]

However the final person moved the final room with including a very close friend giving seven persons to account for
Start over with the math
However that seventh person is very cute and deserves a discount based on looks
Start over with the math

[seanile]

^Id nope right out of there in the wee hours of the day.