Rent Share Problem!

[boynextdoor6]

Hello everyone, Greetings!

I have a problem here, I am trying to solve this for days and I ended up seeking help of experts here! Thanks in advance!

Problem : Rent Share Problem

Description : I need to pay the room rent once in 5 months. I have received the quote from the owner now, i am trying to share it between users but there is a problem. The room is shared by different number of peoples over a period of time. Below figures should help to understand my problem:

				Total Bill	HK$190000
	Start Date	End Date	Tot Days	No of Users (1)	Usage Percent for this period w.r.t total Rent	Rent for this period (2)	Per Person share (2) / (1)
By 2	01-Jun-12	30-Jun-12	30	2
By 3	01-Jul-12	13-Jul-12	13	3
By 4	14-Jul-12	01-Aug-12	19	4
By 3 resto' period	02-Aug-12	30-Sep-12	60	3

Kindly let me know how to share with all users came in and out over period of time, kindly let me know if anymore details required!

Thanks in Advance!

Regards,
Charan
Test Analyst - Cathay Pacific
Hong Kong

 

[boynextdoor6]

Add on for More Clarity

Same person might intersect between the periods. For example:

	Start Date	End Date
By 2	01-Jun-12	30-Jun-12	Charan, Linda
By 3	01-Jul-12	13-Jul-12	C, Ted, James
By 4	14-Jul-12	01-Aug-12	C,T,J,Harris
By 3 resto' period	02-Aug-12	30-Sep-12	C,T,J

Best Regards,
Charan
Test Analyst - Cathay Pacific
Hong Kong

 

[boynextdoor6]

My Workings on this problem

I will Update all my workouts-steps time to time that i am trying so far:

x - Days
y - Persons count

30 x + 2 y = A
13 x + 3 y = B
19 x + 4 y = C
60 x + 3 y = D
A + B + C + D = 190000 (1)


From (1) =>


A = 190000 - B - C - D
B = 190000 - A - C - D
C = 190000 - A - B - D
D = 190000 - A - B - C


From (1) =>


30 x + 2 y +
13 x + 3 y +
19 x + 4 y +
60 x + 3 y = 190000


=> 122 x + 12 y = 190000


From 1 => A + B + C + D = 122 x + 12 y


A = 122 x + 12 y - B - C - D
B = 122 x + 12 y - A - C - D
C = 122 x + 12 y - A - B - D
D = 122 x + 12 y - A - B - C


30 x + 2 y = 190000 - B - C - D
13 x + 3 y = 190000 - A - C - D
19 x + 4 y = 190000 - A - B - D
60 x + 3 y = 190000 - A - B - C (2)


From (2) =>


30 x + 2 y + B + C + D = 190000
13 x + 3 y + A + C + D = 190000
19 x + 4 y + A + B + D = 190000
60 x + 3 y + A + B + C = 190000

 

[boynextdoor6]

Solution!

Since this is a non linear equation, I used bit of interpolation method and solved the problem. Kindly review the attachment and let me know if I am wrong Thanks a million for your time!



Cheers!
Charan
Test Analyst - Cathay Pacific Airways
Hong Kong

 

[HallsofIvy]

You tell us that x is "days" and y is "Persons count" but where did A, B, C, and D come from? Are x and y given and you are trying to solve for A, B, C, and D or vice-versa?
You say "this is a non linear equation" but I see no non-linear equations.

 

[guitarguy]

One thing that might simplify this problem would be to calculate the rent per day. Then consider how many people are sharing which days and write an equation for each time period. A long involved system of linear equations seems cumbersome and overly complex.