The students will need 12 shelves in all.

Step 1
Use the clues to find how many books there are of each kind.

Kind of Book	Books per Shelf	Information From Clue	Number Sentence to Find the Number of Books	Number of Books
Picture	93	The number of picture books is 9 times the number of student dictionaries.	31 × 9 = 279	279
Fiction	63	7 times as many fiction books as biographies	54 × 7 = 378	378
Dictionaries	31	23 fewer dictionaries than biographies	54 – 23 = 31	31
Biographies	27	There are 54 biographies.	54 is given in the clue.	54

Step 2
Write a division sentence to find out how many shelves are needed for each kind of book.

Kind of Book	Number of Books	Books per Shelf	Division Sentence to Find the Number of Shelves (Total Number of Books ÷ Number per Shelf)	Number of Shelves Needed
Picture	279	93	279 ÷ 93 = 3	3
Fiction	378	63	378 ÷ 63 = 6	6
Dictionaries	31	31	31 ÷ 31 = 1	1
Biographies	54	27	54 ÷ 27 = 2	2

Step 3
Add the number of shelves needed for each kind of book to find the total number of shelves needed for the library.
3 + 6 + 1 + 2 = 12 shelves in all