You are right, the text of the case is quite confusing on that.
I think that the "fixed cost/Unit=3$" is just the incidence of the fixed costs per unit sold (total fixed costs/total volume). By definition fixed costs can not be strictly correlated with volumes. For that reason, once that you calculate the fixed costs as 3$/unit*100,000units=300k$, you can assume that they do not vary for the rest of the case.
Is that clear?