109 individuals purchased 109 books for a total value of $2845 \mathrm{Ft}$ to give as gifts. It turned out that only three different prices appeared among the books: $34 \mathrm{Ft}, 27.50 \mathrm{Ft}$, and $17.50 \mathrm{Ft}$. Determine how many books belonged to the first, second, and third price category, knowing that the number of books with the same price did not differ much from each other.