Final answer:
Tomás will need a minimum of 90 tiles to completely cover a 10 feet 6 inches by 8 feet 6 inches floor with 12-inch square tiles, as he can cut them without waste.
Step-by-step explanation:
To calculate the minimum number of tiles Tomás needs to completely cover the floor, we first need to convert the dimensions of the floor from feet and inches to inches, since the tiles are measured in inches. The floor measures 10 feet 6 inches by 8 feet 6 inches, which is equivalent to 126 inches (10 feet × 12 inches/foot + 6 inches) by 102 inches (8 feet × 12 inches/foot + 6 inches). Next, we calculate the area of the floor by multiplying its length by its width, so the floor's area is 126 inches × 102 inches = 12,852 square inches.
Each tile is a square with a side of 12 inches, so the area of one tile is 12 inches × 12 inches = 144 square inches. To find the minimum number of tiles needed, we divide the total area of the floor by the area of one tile: 12,852 square inches / 144 square inches per tile = 89.25 tiles. Since we can't have a fraction of a tile, we round up to the nearest whole number, meaning Tomás needs at least 90 tiles to cover the floor.