Question

The Mazurskys decide to retile their mud room in 18 in. by 18 in. tiles. If their mudroom is 5 ft 6 in. by 13 ft, how many tiles will they need to purchase? They can cut tiles, but they do not want to glue leftover pieces of tiles together to cover any part of the floor.

Answer 1

Answer: 36

Step-by-step explanation:

The tiles are 18 in (1.5 ft) on one side and 18 in (1.5 ft) on the other side.

One width of the room is 5 ft 6 in (5.5 ft), which needs 5.5 /1.5 tiles = 4 tiles (rounded up to the nearest whole tile)

The length of the room is 13 ft, which needs 13 /1.5 tiles = 9 tiles (rounded up to the nearest whole tile)

# of tiles for width x # of tiles for length is 4 x 9 = 36

See the image below, which shows that the tiles in the last row need to be cut down from 1.5 ft to 1 ft and the tiles in the last column need to be cut down from 1.5 ft to 1 ft to fit the measurement of the room:

$\begin {array}{|c|c|c|c|}1.5&1.5&1.5&1\\1.5&1.5&1.5&1\\1.5&1.5&1.5&1\\1.5&1.5&1.5&1\\1.5&1.5&1.5&1\\1.5&1.5&1.5&1\\1.5&1.5&1.5&1\\1.5&1.5&1.5&1\\1&1&1&1\\\end{array}$

Answer 2

The area of one tile is 18 x 18 = 324 square inches.

Convert the dimensions of the room into inches:

5 ft 6 in. = 66 inches.

13 ft = 156 inches.

The area of the room is: 156 x 66 = 10296 square inches.

To find the number of tiles needed, divide the total area of the room by the area of one tile:

10,296 / 324 = 31.78, which means they will need 32 tiles.