what is the price of something if there is 15 and one third feet by 8 and one half feet if the price is $4.75 per foot

I am assuming we are talking about a price in square feet . . .

A = length times width

15 and 1/3 = 46/3

8 and a half = 8.5

$${\frac{{\mathtt{46}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\mathtt{8.5}} = {\frac{{\mathtt{391}}}{{\mathtt{3}}}} = {\mathtt{130.333\: \!333\: \!333\: \!333\: \!333\: \!3}}$$  square feet

So we need to purchase 131 square feet's worth (assuming they don't deal in fractions).

131*4.75 = $622.25