Applied math problem: library collection development

First of all, this is my first post here. I struggled with forum selection. If there is a more appropriate forum, I hope mods will assist me in moving the thread.

I am using "relative use" to determine a "demand" variable to assist me in allocating my library materials budget between various component collections.

u = number of times books are picked up or "used" for each component collection

v = number of volumes, or books, in a component collection

U = total number of uses for all component collections

V = total number of volumes in all component collections

r = relative use, or (u/v)/(U/V)

d = demand, or (u*r) for each component collection.

The problem is that it is not behaving how I would expect: the sum total of the demands of all component collections does not equal the demand for the entire collection as a whole. Where is my math going wrong, if this expectation is correct?

Here are my numbers (space delimited, please tell me if there is a better way to display this). I've been using a spreadsheet for this.

Collection u v r d

Fiction 15716 8818 1.13 17765

LP Fiction 948 725 0.83 786

Mystery 6150 3822 1.02 6276

LP Mystery 220 219 0.64 140

SciFi 1639 1704 0.61 1000

SS 358 403 0.56 202

Western 458 475 0.61 280

Total Demand: 25,489

Sum of component Demands: 26,449

Shouldn't these be the same?