Answer: The cost to tile the floor is $318.24.
Step-by-step explanation:
Since we have given that
Dimensions of floor is 12 by 17 foot.
So, Area of floor would be
![12\times 17\\\\=204\ sq.\ foot](https://tex.z-dn.net/?f=12%5Ctimes%2017%5C%5C%5C%5C%3D204%5C%20sq.%5C%20foot)
As we know that 1 foot = 12 inch
So, Area of floor would be
![204\times (12)^2\\\\=204\times 144\\\\=29376\ sq.\ foot](https://tex.z-dn.net/?f=204%5Ctimes%20%2812%29%5E2%5C%5C%5C%5C%3D204%5Ctimes%20144%5C%5C%5C%5C%3D29376%5C%20sq.%5C%20foot)
Dimension of brick tiles is given by
![3\dfrac{5}{8}\ by\ 7\dfrac{5}{8}\ by\ \dfrac{1}{2}](https://tex.z-dn.net/?f=3%5Cdfrac%7B5%7D%7B8%7D%5C%20by%5C%207%5Cdfrac%7B5%7D%7B8%7D%5C%20by%5C%20%5Cdfrac%7B1%7D%7B2%7D)
So, Area of brick tiles is given by
![2(lb+bh+lh)\\\\=2(\dfrac{29}{8}\times \dfrac{61}{8}+\dfrac{61}{8}\times \dfrac{1}{2}+\dfrac{29}{8}\times \dfrac{1}{2})\\\\=2(\dfrac{1769}{64}+\dfrac{61}{16}+\dfrac{29}{16})\\\\=2\times \dfrac{1769+244+116}{64}\\\\=\dfrac{2129}{32}](https://tex.z-dn.net/?f=2%28lb%2Bbh%2Blh%29%5C%5C%5C%5C%3D2%28%5Cdfrac%7B29%7D%7B8%7D%5Ctimes%20%5Cdfrac%7B61%7D%7B8%7D%2B%5Cdfrac%7B61%7D%7B8%7D%5Ctimes%20%5Cdfrac%7B1%7D%7B2%7D%2B%5Cdfrac%7B29%7D%7B8%7D%5Ctimes%20%5Cdfrac%7B1%7D%7B2%7D%29%5C%5C%5C%5C%3D2%28%5Cdfrac%7B1769%7D%7B64%7D%2B%5Cdfrac%7B61%7D%7B16%7D%2B%5Cdfrac%7B29%7D%7B16%7D%29%5C%5C%5C%5C%3D2%5Ctimes%20%5Cdfrac%7B1769%2B244%2B116%7D%7B64%7D%5C%5C%5C%5C%3D%5Cdfrac%7B2129%7D%7B32%7D)
So, Number of clay brick would be
![29376\div \dfrac{2129}{32}\\\\=29376\times \dfrac{32}{2129}\\\\=\dfrac{29376\times 32}{2129}\\\\=441.53\\\\\approx 442](https://tex.z-dn.net/?f=29376%5Cdiv%20%5Cdfrac%7B2129%7D%7B32%7D%5C%5C%5C%5C%3D29376%5Ctimes%20%5Cdfrac%7B32%7D%7B2129%7D%5C%5C%5C%5C%3D%5Cdfrac%7B29376%5Ctimes%2032%7D%7B2129%7D%5C%5C%5C%5C%3D441.53%5C%5C%5C%5C%5Capprox%20442)
cost of each clay brick = $0.72
So, Total cost of flooring would be
![442\times 0.72\\\\=\$318.24](https://tex.z-dn.net/?f=442%5Ctimes%200.72%5C%5C%5C%5C%3D%5C%24318.24)
Hence, The cost to tile the floor is $318.24.