The correct statement modeled by the expression \( \frac{150}{k} \) is:
A librarian had 150 books to be placed on shelves with an equal number of books on each shelf. If k is the number of shelves to be used, then \( \frac{150}{k} \) is the number of books on each shelf.
This is because dividing the total number of books (150) by the number of shelves (k) gives the number of books per shelf.