House Payment Equation

[RyanFoy]

Have have 6 people that are renting a house. Some of them have larger rooms and one has a master bed room with his own bathroom and walk in closet.
I want to setup a percent payment method to resolve this issue. I seem to be a little off and can't find my mistake. Please send help.

Base amount 100/6 = 16.66666667

I want to give two people a 5% increase and one person a 8% increase.

Person 1,2 & 3	Person 4 8%	Person 5 & 6 5%
13.66666667 =100/6-((10/6)+(8/6))	23 =((100/6)+8)-(10/6)	21.16666667 =(100/6+5)-(8/6)+5/6
106.3333333 =(Person 1,2&3*3)+(Person 4)+(Person 5&6*2)

I seem to be missing something or not setting this up correctly.

 

[tkhunny]

I'll just give you one for free. I cannot tell what it is you are doing to find a solution.

You'll have to deal with the minor rounding issues.

Starting Base Amount that assumes everyone pays the same.
16.6666
16.6666
16.6666
16.6666
16.6666
16.6666
---------
100.0000 (Theoretically)

The individual increases:
16.6666 * 1.05 = 17.5
16.6666 * 1.05 = 17.5
16.6666 * 1.08 = 18.0
16.6666
16.6666
16.6666
---------
103.0000 (Theoretically)

Estimate the increase to check: (5 + 5 + 8 + 0 + 0 + 0)/6 = 18/6 = 3. Thus, about a 3% increase. Your 6% increase should have set off alarms.

Scale back to 100% Total (Unless you're planning to pocket the excess).
17.50 / 1.03 = 16.9903
17.50 / 1.03 = 16.9903
18.00 / 1.03 = 17.4757
16.6666 / 1.03 = 16.1812 <== This is the REAL Base Amount.
16.6666 / 1.03 = 16.1812 <== The amount paid by those with no surcharge.
16.6666 / 1.03 = 16.1812
---------
100.0000 (Theoretically)

Check validity:
16.9903 / 16.1812 = 1.05 - Perfect
17.4757 / 16.1812 = 1.08 - Perfect

You weren't expecting the ones with no increase to pay the same amount they started with, were you? Given a fixed total amount, if someone has to pay more, someone else gets to pay less.

Note: It is a little weird that your 5% increase is really only 1.9% increase from the original "base amount". 16.9903/16.6666 = 1.0194. Rest assured that it is a 5% increase over the real "Base Amount".

 

[RyanFoy]

I think I was just over complicating the matter. Thank you.

 

[Steven G]

Here is how I would have approached this problem
Let x= amount one pays without the surcharge.
So we need x+x+x+1.05x + 1.05x + 1.08x = 6.18x=100%

So x= 100/6.18 % = 16.1812297735%
1.05x = 16.9902912621%
and 1.08 x =17.4757281554%

 

[tkhunny]

Here is how I would have approached this problem

Indeed. Algebra vs. Spreadsheet. This is why I have my signature.