The manager already hired 9 people. Let 
 be the number of people he still can hire. Since these people will add to the 9 he already hired, when the hiring campaign will be over he will have hired 
 people. We know that he can't hire more than 14 people, so the number of people hired must be less than or equal to 14:

If we subtract 9 from both sides, we have

so, the manager can hire at most 5 other people