# Minimum cost incurred for covering the floor with tiles

Alex plans to cover a rectangular floor of dimensions 9.5 meters and 11.5 meters using tiles. Two types of square shaped tiles are available in the market. A tile with side 1 meter costs 100 dollars and a tile with side 0.5 meters costs 30 dollars . The tiles can be cut if required. What will be the minimum cost of covering the entire floor with tiles? (Assume cost of cutting to be 0)

My approach:-

Firstly I noticed that a 1x1 tile could be divided into 4 (0.5x0.5) tiles. Now we know the cost of 1x1 tile is 100, and cost of 4 (0.5 x 0.5) tiles would be 30 * 4 =120 ,

therefore it would be economical to use as many 1x1 tiles as possible in case of covering, so I ended up with the following diagram, having complete 1x1 tiles used for area = 11 * 9 = 99 m$$^2$$ , , there are (11 * 9) tiles of 1x1 dimension used and each tile would cost 100 , so therefore the cost of these 99 tiles would be 9900 dollars.

Now for the remaining 0.5 m gaps instead of fitting (0.5 x 0.5) tiles , what I did was to use the 1x1 tile only and cut it into tiles of (1x0.5) and fill it in the spaces left

Number of (1x0.5) tiles required in the very last column = 9 Number of (1x0.5) tiles required in the very bottom row = 11 therefore total number of (1x0.5) tiles = 20 , and these can be obtained from 10 (1x1) tiles therefore a total of (10*100) dollars more = 1000 dollars , so my answer would become 9900+1000=10900 dollars , but the answer is 10930 dollars

Area of floor = 109.25 m$$^2$$
Cost of covering 109 m$$^2$$ (with 1x1 tiles) = 10900 dollars
Cost of covering 0.25 m$$^2$$ (with 0.5x0.5 tile)= 30 dollars