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here is some data for 4 variables:

State:population:num_schools:size

A:100k:10:500

B:90k:20:350

C:125k15:450

D:300k:40:900

And here is a national sales number: 500k

I'm want to distribute the 500k to the state level using the variables above.

I could distribute the national data according to the "distribution" (the percentage in each state) of each of these variables individually, like so:

State:%population:%num_schools:%size

A:.16:.12:.23

B:.15:.23:.16

C:.20:.18:.20

D:.49:.47:.41

So for state A, 16% of sales would be assigned based on the population data, 12% based on number of schools in the state, but 23% based on the size variable (similarly for the other states). The point is each variable will distribute the 500k differently (500k*%population will be differently distributed than 500k*%size)

So my question is: How can I combine these variables so that my national data (the 500k) is distributed according to a combined factor of these various variables? How do I combine them to get a single factor given that they are on different scales (one is population which is in the '000s, another is in the 100's, etc). Do I simply multiply the percentages (from the second table) together to get a combined factor? (For example, state A's factor would be: 16*.12*.23 =.004). I know that is wrong..but I don't know how to do it correctly.

Any help how to approach this, in particular how to build a combined factor, will be appreciated.