CASHIER HAS A TOTAL OF 39 BILLS CONSISTING OF ONES, FIVES, AND TWENTIES. THE NUMBER OF TWENTIES IS 16 LESS THAN THE NUMBER OF ONES. THE TOTAL VALUE IS $208. HOW MANY OF EACH DENOMINATION IS THERE.

Just list the facts as given:

u+f+t = 39
t = u-16
u+5f+20t = 208

Now just solve as usual