A room that measures 6m x 9m is to be covered with floor tiles. The tile depot has the following sizes and price for the available tiles: 48cm x 48cm @ Php 97.00 and 36cm x 36 cm @ Php 85.00. If all other materials ( adhesive and cement ) cost is constant, which tile size will be more economical to use? Explain your choice.
Answers
Given:
Surface area of room = 6 m x 9 m
Surface area of tile 1 = 48 cm x 48 cm
Price per piece for tile 1 = Rs. 97.00
Surface area of tile 2 = 36 cm x 36 cm
Price per piece for tile 2 = Rs. 85.00
To find:
Economical tile=?
Formula:
Cost for putting tiles in floor = No. of tiles required x cost of each tile
Steps
The surface area of the room is given by the product of 6 m with 9 m
Surface area of room = 6 m x 9 m
Then, the surface area of the room = 54 m².
In case of tile 1, the surface area for each tile in tile 1 is
Surface area for tile 1 = 48 cm x 48 cm = 2304 cm²
Surface area for tile 1 =
Surface area for tile 1 = 0.2304 m²
Then, number of tiles required for tile 1 to cover the given floor room is
Number of tile 1 required =
Number of tile 1 required = 234 tiles
As each tile cost Rs. 97.00 in case of tile 1, then the total cost required to cover the floor with this tile1 is
Total cost for tile 1 =234 x 97
Total cost for flooring using tile 1 = Rs.22734 ------------------(1)
Similarly, in case of tile 2, the surface area for tile 2 will be
Surface area for tile 2 = 36 x 36 = 1296 cm²
Surface area for tile 2 in metres = 0.1296 m²
Number of tiles 2 required to floor the room =
As 417 tiles are required for completing flooring of room, the total cost required to buy tiles 2 is
Total cost = 417 x 85 = Rs. 35445 -------------------------------(2)
From (1) and (2), it can be seen that cost of flooring the room with tile 1 is Rs. 22374 while flooring the room with tile 2 is Rs. 35445. Thus, the tiles with size 48 cm x 48 cm will be more economical to use as we can use less number of tiles in this case and the cost of flooring will also be less.