Geographic Factor equations

[CzechCzar]

Hi all,

I think that calculus is the proper forum for this. Apologies if it's not.

I am trying to solve a system of compensation equations to find the median compensation multiplied by a geographic factor. For instance, it is more expensive to live in San Francisco rather than Reno, so the factor for San Francisco will be higher. The actual compensation is known in all cases, and I am trying to determine whether I can solve for the median (the same in all equations) and the geographic factor (different in all equations).

My three equations are:

95,964 = (x)(A)
96,799 (x)(B)
124,416 = (x)(C)

How would I do this?

 

[DrPhil]

Hi all,

I think that calculus is the proper forum for this. Apologies if it's not.

I am trying to solve a system of compensation equations to find the median compensation multiplied by a geographic factor. For instance, it is more expensive to live in San Francisco rather than Reno, so the factor for San Francisco will be higher. The actual compensation is known in all cases, and I am trying to determine whether I can solve for the median (the same in all equations) and the geographic factor (different in all equations).

My three equations are:

95,964 = (x)(A)
96,799 = (x)(B)
124,416 = (x)(C)

How would I do this?

You have four unknowns and three equations, so you can't find them all without another relationship. You CAN find the ratios of A : B : C = 1 : 1.009 : 1.296

Those ratios can be normalized any way you want .. what I have done for simplicity is compare all to the lowest value. If you accept that normalization, then X = 95,964.

 

[CzechCzar]

That is what I thought. Thanks!

You have four unknowns and three equations, so you can't find them all without another relationship. You CAN find the ratios of A : B : C = 1 : 1.009 : 1.296

Those ratios can be normalized any way you want .. what I have done for simplicity is compare all to the lowest value. If you accept that normalization, then X = 95,964.