## Problem of the Month - March 2011Sally wants to do a home improvement project. Her kitchen floor is in bad shape and she wants to retile the floor. She needs to figure out how many tiles to buy. Her kitchen measures 15’ by 20’. She will use tiles that measure 13” by 13”. The tile costs $3.50 per square feet. How many tiles does she need to buy and how much will the tiles cost? ## Answer
The kitchen is 15’ by 20’. The area of the kitchen is: Kitchen area = 15’ x 20’ = 300 square feet
The tiles measure 13” by 13”. We need to convert this to feet. 1 foot = 12 inches. So the area of one tile is: Area of one tile = 13” x 13” = (13/12)’ x (13/12)’ = 1.08’ x 1.08’ = 1.17 square feet
Since the area of the kitchen is 300 square feet, and the area of one tile is 1.17 square feet, it seems that we need (300/1.17) = 256 tiles to cover the entire kitchen area. However, when you tile a room, the tiles usually do not line up exactly to edges of the room. You will likely need to cut the tile to fit the width and length of the room. As a result, you would need more tiles and it is important to take that into account. Here for example the room is 15 feet wide, which means is it 15/1.08 = 13.9 tiles wide. It will take 14 tiles to cover it width-wise, and one tile will need to be cut. Its length is 20 feet, which means it takes 20/1.08=18.5 or in other words 19 tiles to cover in length-wise. Hence it will take 14x19 = 266 tiles when you calculate it this way, which is more correct. Other corrections you can worry about include things like tile spacing. Smaller tiles are spaced by 1/8”, while larger ones are spaced ¼” or even ½”; this reduces slightly the amount of tile you need to cover the room.
We know we need to buy 266 tiles. Each tile costs $3.50 per square feet. So the total cost is: Total cost = Area of the tiles x $3.50 = 266 x 1.17 (square feet per tile) x $3.50 (per square feet) = $1,089 Let’s assume in addition there is a sales tax of 8% Sales tax = $1089 x 8% = $1089 x 0.08 = $87 Total cost including sales tax = $1,176 So to tile the kitchen, Sally needs to buy 266 tiles and it would cost her almost $1,200.00 just for the cost of the tile. |

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