Friendly Fighter

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Okay, this one is driving me batty..

How are bonuses to d20 rolls calculated? I was under the impression that all variables are added together, and the total is the bonus (or penalty) you would receive, with there being no way to modify a number on the back end.

Example.

We have a player whom is trying to use Agile Maneuvers and Fury's Fall to affect his CMB.

Agile maneuvers replaces your strength with your dexterity for figuring out your CMB.

Fury's Fall allows you to add your dex to your CMB when making a trip attempt.

As I see it, the equation would using these two feats would be as follows

BaB+Dex (agile maneuvers)+Dex (Furys fall)+Size+Misc=CMB. This of course would mean that his dex bonus would only stack once.

He is reading it as follows

BaB+Dex (agile maneuvers)+size=CMB+Dex (Furys fall).

Which (if any) is correct? and to further broaden the question which/what would be the correct way for calculating bonuses? Does anything ever add to the final/backend number?