To solve this problem, we can use the concept of division.
Given that an average of 35 paperback books fit on each shelf, and there are 4 shelves in each bookcase, we can calculate the total number of books that can be accommodated in one bookcase using the formula:
Total number of books in one bookcase = Number of shelves in one bookcase × Number of books per shelf
Plugging in the given values, we have:
Total number of books in one bookcase = 4 shelves × 35 books per shelf
Total number of books in one bookcase = 140 books
Now, we need to find the number of bookcases needed to shelve 1540 books. We can do this by dividing the total number of books by the number of books in one bookcase:
Number of bookcases needed = Total number of books / Total number of books in one bookcase
Number of bookcases needed = 1540 books / 140 books
Using long division, we find that 1540 divided by 140 equals 11 with a remainder of 0. This means that all the books can be evenly distributed among the bookcases.
Therefore, the correct answer is C) 11.