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