Question

Bob is tiling the floor of his 12 foot by 16 foot living room. He plans to place one-foot by one-foot square tiles to form a border along the edges of the room and to fill in the rest of the floor with two-foot by two-foot square tiles. How many tiles will he use?

Answer 1

(12×2)+(14×2)=52___the area around the border

1×1=1_____the area of tiles around the border

52÷1=52_______number of tiles

(12-2)×(16-2)=140

2×2=4

140÷4=35

52+35=87

Answer 2

To calculate how many tiles Bob will use, we first need to determine the area of the living room and then subtract the area of the border tiles.

1. Calculate the area of the living room: The living room is 12 feet by 16 feet, so the area is: Area = Length x Width Area = 12 feet x 16 feet Area = 192 square feet

2. Calculate the area of each 2-foot by 2-foot tile: Each tile has an area of 2 feet x 2 feet = 4 square feet.

3. Calculate the area of the border tiles: Since the border tiles are 1-foot by 1-foot, they cover a strip 1 foot wide around the perimeter of the room. This strip will be the same on all sides.

   The length of the border on the long sides of the room (16 feet) will be covered by 16 border tiles. The length of the border on the short sides of the room (12 feet) will be covered by 12 border tiles.

   Therefore, the total area covered by the border tiles is: (16 feet x 1 foot) + (12 feet x 1 foot) = 16 square feet + 12 square feet = 28 square feet

4. Subtract the area of the border tiles from the total area of the room to find the area covered by the 2-foot by 2-foot tiles: 192 square feet (total area) - 28 square feet (border area) = 164 square feet

5. Calculate the number of 2-foot by 2-foot tiles needed to cover the remaining floor area: 164 square feet ÷ 4 square feet/tile = 41 tiles

So, Bob will use a total of 41 tiles to tile the floor of his living room with one-foot by one-foot border tiles along the edges and two-foot by two-foot tiles for the rest of the floor.