Well, if there is no restriction on how it is solved, the easiest way is to solve by guess and adjustment.
Assume everyone bought coach tickets, then expense=15*220=3300 So there is (12930-3300)=9630 left over for them to switch to first class. The number employees who can switch to first class =9630/(1290-220) =9630/1070 =9 So there are 9 first-class tickets and (15-9)=6 coach tickets.