The number of rabbits was 80+34 = <<80+34=114>>114
The total number of rabbits and antelopes is 114+80 = <<114+80=194>>194
The number of hyenas was 42 fewer than the combined number of antelopes and rabbits, which is 194-42 = 152
The number of wild dogs was 50 more than the number of hyenas, that is 152+50= 202
The number of leopards is 1/2*114 = <<1/2*114=57>>57
The total number of animals Josie saw is 57+202+152+114+80 = <<57+202+152+114+80=605>>605
#### 605