The CBO report (.pdf) puts the first number I've seen on the number of "security contractors" in the Iraq theater: 30,000. That's one mercenary for every six U.S. soldiers.
The cost rationale:
The costs of a private security contract are comparable with those of a U.S. military unit performing similar functions. During peacetime, however, the private security contract would not have to be renewed, whereas the military unit would remain in the force structure.