Question

Sally is arranging her books on shelves. She has 16 adventure books, 32 mysteries, and 12 biographies. She wants each shelf to have the same number of each type of book. What is the greatest number of shelves that Sally will use if she puts all the books on shelves? How many of each type of book wil be on each shelf?

Answer 1

The most SHE can have is 4 cabinets. There will be 3 biographies on each shelf, 4 adventure books, and 8 mysteries

Answer 2

She needs 4 shelves. The number of books in each shelf are: 4 adventure books, 8 mysteries books, and 3 biographies books.

Explanation:

Consider the provided information.

Sally is arranging her books on shelves. She has 16 adventure books, 32 mysteries, and 12 biographies.

We need to find the greatest number of shelves that Sally will use if she puts all the books on shelves.

First calculate the GCF of the provided number as shown:

16 = 2×2×2×2

32 = 2×2×2×2×2

12 = 2×2×3

The GCF = 2×2 = 4.

Hence, she needs 4 shelves.

Now find how much of each type of book will be on each shelf.

There are 16 adventure books for 4 shelves, that means each shelves should have 4 adventure books.

There are 32 mysteries books for 4 shelves, that means each shelves should have 8 mysteries books.

There are 12 biographies books for 4 shelves, that means each shelves should have 3 biographies books.

Hence, the number of books in each shelf are 4 adventure books, 8 mysteries books, and 3 biographies books.