Bookshelf Bedlam

Solution

The students will need 12 shelves in all.

Explanation

Step 1

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

Kind of Book Books per Shelf Information from Clue Number Sentence to Find the Number of Books Number of Books
Picture 93 9 times the number of dictionaries 31 x 9 = 279 279
Fiction 63 7 times as many fiction books as biographies 54 x 7 = 378 378
Dictionaries 31 23 fewer dictionaries than biographies 54 − 23 = 31 31
Biographies 27 54 biographies 54 given in 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