Each carton has an area of 4*4*5 = <<4*4*5=80>>80 square inches.
Each shipping box has an area of 20*20*20 = <<20*20*20=8000>>8000 square inches
The total number of cartons that will fit into each box is 8000/80 = <<8000/80=100>>100
Since there are 3 widgets in each carton, the total number of cartons in each box will be 3*100 = <<3*100=300>>300
#### 300