Final answer:
To cover the countertop, 454 4-inch by 4-inch ceramic tiles would be needed when including an extra 5% for waste, after converting the countertop dimensions to inches and calculating the total area. Tiles are then rounded up to the nearest whole tile.
Step-by-step explanation:
The question asks how many 4-inch by 4-inch ceramic tiles are needed to cover an 8 ft by 6 ft countertop, including an extra 5% to account for waste. To find the number of tiles needed, we first convert the countertop dimensions from feet to inches, since the tile dimensions are given in inches. There are 12 inches in a foot, so the countertop measures 96 inches (8 ft x 12 in/ft) by 72 inches (6 ft x 12 in/ft). Next, we calculate the area of the countertop in square inches, which is 96 inches x 72 inches = 6,912 square inches.
The area of one tile is 4 inches x 4 inches = 16 square inches. To cover the countertop, we divide the total area of the countertop by the area of one tile: 6,912 square inches ÷ 16 square inches/tile = 432 tiles. Since we need to buy an extra 5% for waste, we multiply the number of tiles needed by 1.05 (100% + 5% = 105%). This gives us 432 tiles x 1.05 = 453.6 tiles. As we cannot buy a fraction of a tile, we round up to the nearest whole tile, resulting in 454 tiles.