Can the Sum of Two Unknown Variables be Determined with Limited Information?

[arch1]

Hi there, I need help with the following situation. Apologies if I'm not using the correct arithmetic terms!

Variables: d,e,f
e + f = g
d / g = j
j x e = K
j x f = L
K + L = M
d = M

the above situation is a simplified problem, which is easily solvable. Here's where I run into trouble: (bottom row is the sum)
[TABLE="class: grid, width: 500, align: center"]
[TR]
[TD]d[/TD]
[TD]e[/TD]
[TD]f[/TD]
[TD]g= e+f[/TD]
[TD]j=d/g[/TD]
[TD]K=j x e[/TD]
[TD]L=j x e[/TD]
[TD]M = K+ L[/TD]
[/TR]
[TR]
[TD]1500[/TD]
[TD]0[/TD]
[TD]1500[/TD]
[TD]1500[/TD]
[TD]1.000[/TD]
[TD]0[/TD]
[TD]1500[/TD]
[TD]1500[/TD]
[/TR]
[TR]
[TD]2673[/TD]
[TD]1250[/TD]
[TD]1150[/TD]
[TD]2400[/TD]
[TD]1.113750[/TD]
[TD]1392[/TD]
[TD]1281[/TD]
[TD]2673[/TD]
[/TR]
[TR]
[TD]2729[/TD]
[TD]2366[/TD]
[TD]0[/TD]
[TD]2366[/TD]
[TD]1.153423[/TD]
[TD]2729[/TD]
[TD]0[/TD]
[TD]2729[/TD]
[/TR]
[TR]
[TD]6902[/TD]
[TD]3616[/TD]
[TD]2650[/TD]
[TD]6266[/TD]
[TD][/TD]
[TD]4121[/TD]
[TD]2781[/TD]
[TD]6902[/TD]
[/TR]
[/TABLE]


But 6902/6266 = 1.101500 and j x e for the totals is 3,983 and j x f is 2,919

Is there a formula where I can take the sum of e and f and multiply by j or some other factor and get the correct 4,121 and 2781? without knowing the individual numbers that make up the total of e and f? Multiplying 3616 and 2650 by 1.101500 gives me the wrong values for K and L, even though the sum of the two numbers is 6,902.

Thanks!

 

[Ackbach]

Yeah, it's just not the case that if, say, $z=\dfrac{x}{y}$, that therefore $z_1 + z_2 = \dfrac{x_1 + x_2}{y_1 + y_2}$. The problem is the division. If you only had multiplication going on, you might get away with it on a small scale (but beware of properly multiplying!) In other words, the properties of individual rows in your spreadsheet before you take the sum are not necessarily the properties of the sum row.

I might be able to help you out more if you gave the bigger context of how this problem originated.

 

[arch1]

The problem originates as requirement for measuring certain types of building areas. The standard, insists we calculate and sum using a certain method. I would ideally like to be able to look at the last row in the chart:
6902 3616 2650 6266 4121 2781 6902

And be able to use those numbers without having to deal with each row of each column. It would massively help when writing summaries.
so if i could take:

6902/6266 = 1.1015

3616 x (1.1015?) = 4121 somehow...
and
2650 x (1.1015?) = 2781 somehow...

and 4121 + 2781 = 6902
but so does 3983 + 2919 = 6902
3983 and 2919 unfortunately, do not help - ideally if i can find a way to 4121 and 2781

Thanks!

 

[arch1]

The problem originates as requirement for measuring certain types of building areas. The standard, insists we calculate and sum using a certain method. I would ideally like to be able to look at the last row in the chart:
6902 3616 2650 6266 4121 2781 6902

And be able to use those numbers without having to deal with each row of each column. It would massively help when writing summaries.
so if i could take:

6902/6266 = 1.1015

3616 x (1.1015?) = 4121 somehow...
and
2650 x (1.1015?) = 2781 somehow...

and 4121 + 2781 = 6902
but so does 3983 + 2919 = 6902
3983 and 2919 unfortunately, do not help - ideally if i can find a way to 4121 and 2781

Thanks!

Someone emailed to help me with this problem:

This is a common math problem of more unknowns than correlated knowns. (Underdetermined System). K and L are two unknowns in one equation and requires another equation to relate K or L to the whole to make the situation possible. In addition, j is based off of a weighted disproportion in lines 1, 2 and 3 (having taken values of 1, 1.113, and 1.15), meaning that value is not weighted the same if done at the level of the sum.
The reason you get M the same because it took on the weight of the total from knowing what d was which is the same number for M, the factor j is the proportional increase from e and f to get to M from a average j value.

In short, this is not possible unless more information is provided about the individual cells to obtain individual summed K and L values.

So it does not seem possible to find the solution? Anyone see any flaws in the reasoning above?

Thanks!