To calculate the number of tiles needed to cover the cafeteria floor, we first need to convert the dimensions of the cafeteria into centimeters, since the side length of the tiles is given in centimeters:
Length of cafeteria in cm = 30 m x 100 cm/m = 3000 cm
Width of cafeteria in cm = 20 m x 100 cm/m = 2000 cm
Next, we can calculate the area of the cafeteria floor in square centimeters:
Area of cafeteria floor = Length x Width = 3000 cm x 2000 cm = 6,000,000 cm^2
Finally, we can calculate the number of tiles needed by dividing the area of the floor by the area of each tile:
Area of each tile = 50 cm x 50 cm = 2500 cm^2
Number of tiles needed = (Area of cafeteria floor) / (Area of each tile) = 6,000,000 cm^2 / 2500 cm^2 = 2400 tiles
Therefore, 2400 tiles are needed to cover the cafeteria floor.