A carpenter has been hired to cover a 12-foot by 14-foot kitchen with an arrangement of 2-inch square tiles along the outside edges of the floor and 8-inch square tiles for the rest of the floor. The 8-inch square tiles come 24 in a box and the 2-inch square tiles come 48 in a box.

Question

A carpenter has been hired to cover a 12-foot by 14-foot kitchen with an arrangement of 2-inch square tiles along the outside edges of the floor and 8-inch square tiles for the rest of the floor. The 8-inch square tiles come 24 in a box and the 2-inch square tiles come 48 in a box.

Answer 1

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Answer 2

To find out how many 8-inch square tiles are needed to cover the kitchen floor, we first need to calculate the total area of the floor. The area of a rectangle can be found by multiplying its length by its width.

In this case, the length of the kitchen floor is 12 feet, which is equivalent to 144 inches (since 1 foot = 12 inches). The width of the kitchen floor is 14 feet, which is equivalent to 168 inches. So, the total area of the floor is 144 inches * 168 inches = 24,192 square inches.

Next, we need to subtract the area covered by the 2-inch square tiles along the outside edges. Since the tiles are arranged along the outside edges, there will be tiles on all four sides of the floor. Each side will require 2 tiles, so the total number of tiles needed for the outside edges is 2 tiles * (12 tiles + 14 tiles) = 52 tiles.

To find the remaining area to be covered by the 8-inch square tiles, we subtract the area covered by the outside edge tiles from the total floor area: 24,192 square inches - (52 tiles * 2-inch * 2-inch) = 24,192 square inches - 416 square inches = 23,776 square inches.

Now, we divide the remaining area by the area covered by each 8-inch square tile to determine the number of tiles needed. The area covered by each tile is 8 inches * 8 inches = 64 square inches.

Therefore, the number of 8-inch square tiles needed is 23,776 square inches / 64 square inches = 372.5 tiles.

However, since tiles cannot be split or fractional, we need to round up to the nearest whole number. So, a total of 373 tiles are needed.

Given that there are 24 tiles in each box of 8-inch square tiles, the number of boxes needed to cover the kitchen floor is 373 tiles / 24 tiles per box = 15.54 boxes.

Again, we need to round up to the nearest whole number, so a total of 16 boxes of 8-inch square tiles are needed to cover the kitchen floor.