Minus' Solution to

Tile Tally
Posted Weeks of March 16 - 29, 1998

Tim can lay the tiles down so that there are 84 along the narrower side, and 120 along the longer side. In total, since each tile has an area of 0.25 m², and the total area is 2520 m², there will be 10,080 tiles.

With the carpet squares, there will be 70 along one side, and 100 along the other side. Since each carpet square has an area of 0.36 cm², there will be 7000 carpet squares. Thus, there are 3080 more tiles than carpet squares.

Each diamond has a side of 0.6/ m, so the area of each diamond is 0.18 m². Since there are 7000 diamonds (given that there are 7000 carpet squares), the total area covered by diamonds is 1260 m². Or, more simply, each diamond occupies half of a carpet square, so there is 2520(1/2) = 1260 m² covered by diamonds.

Daniel Sheehan, of Christ Church Grammar School in Western Australia, supplied our fiesty old mascot with this mmmmighty fine solution. Daniel didn't give us an answer to the bonus question, but we'll give him bonus marks for his attention to detail.

First of all we have to convert the floor measurements of 42 m x 60 m into cm which is 4200 cm x 6000 cm. Now we can divide the lengths of the floor by the side lengths of the tiles because they are both in the same measurements.

We divide 4200 cm by 50 cm to get the number of ceramic tiles to be laid on one length of the floor, which equals 84 tiles. We divide 6000 cm by 50 cm to get the other length of the floor, which equals 120 tiles. Now we multiply 84 tiles by 120 tiles to get the total number of ceramic tiles, which is 10080 tiles.

For the number of carpet tiles we do exactly the same as we did for the ceramic tiles but divide the lengths by 60 cm instead of 50 cm. 4200cm divided by 60 equals 70 tiles for one length, and 6000cm divided by 60 equals 100 tiles for the other length. 70 x 100 equals 7000 carpet tiles required to cover the floor. Now we must subtract 7000 from 10080 because the question asks us how many more ceramic tiles are needed that carpet ones. The answer is 3080 tiles.

First students converted the 42 m x60 m to 4200 cm x 6000 cm, and found the area of the floor to be 25,200,000 sq.cm.  The area of each piece of tile was 2,500 cm and the area of each carpet square was 3600 sq.cm.  The floor area was divided by each of the other areas to find that 10,080 tile squares were needed and 7000 carpet square were needed.  To find how many more tiles were needed subtract 7000 from 10,800 to get 3,080 more tile squares.

Bonus:  Since 7000 carpet squares were needed and each square had an area of 3,600, we found that the total area of the carpet squares was 25,200,200, or the area of the room.  The diamond took up half of the carpet square, so we divided 25,200,000 in half to find that the diamonds took up 12,600,000 sq. cm.

We know that 1 m = 100 cm. Therefore, the floor area is 4200 cm x 6000 cm. So for ceramic tiles, we can fit 4200/50 = 84 tiles in the width and 6000/50 = 120 tiles in the length. Therefore total ceramic tiles needed are  84 x 120 = 10080 .

For carpet tiles, we need 4200/60 = 70 tiles in the witdh and 6000/60 = 100 tiles in the length, so to cover the area we need 70 x 100 = 7000 carpet tiles in all. Therefore we need 10,080 - 7,000 = 3,080 more ceramic tiles than carpet tiles.

Bonus question: Since each diamond pattern is 1/2 the area of each carpet square, therfore 1/2 the total floor space will be covered by diamonds, that is (42 m x 60 m)/2 = 1260 square meters.