You borrow bookcases, to display 943 books at a book sale. You plan to put 22 books on each shelf. No books will be on top of the bookcases.
a. How many bookcases must you borrow to display all the books?
You need ___ bookcases.
b. You fill the shelves of each bookcase in order, starting with the top shelf. How many books are on each shelf of the last bookcase?
Top shelf: ____ books
Second shelf: ____ books
Third shelf: _____ books
Fourth shelf: _____ books
Bottom shelf: _____ books
a. You need 9 bookcases.
b.
22 books
22 books
19 books
0 books
0 books
a. To determine the number of bookcases needed, divide the total number of books by the number of books per shelf:
943 books ÷ 22 books per shelf = 42.8636
Since you cannot have a fraction of a bookcase, you need to round up to the nearest whole number. Therefore, you would need to borrow 43 bookcases.
So, you need 43 bookcases.
b. Since each bookcase has the same number of shelves, divide the total number of books by the number of shelves per bookcase to determine the number of books on each shelf of the last bookcase:
943 books ÷ 43 bookcases = 21.9767
Again, you cannot have a fraction of a book on a shelf, so round up to the nearest whole number. The last bookcase will have the remaining books distributed on its shelves, with some shelves potentially having one extra book compared to the others.
Therefore, the number of books on each shelf of the last bookcase will vary. The exact distribution will depend on the total number of books and the number of shelves per bookcase.
a. To find out how many bookcases you need to borrow to display all the books, you can divide the total number of books by the number of books that can fit on each shelf.
Total number of books: 943
Number of books on each shelf: 22
To find the number of bookcases, divide the total number of books by the number of books on each shelf:
943 / 22 = 42.863636...
Since you can't have a fraction of a bookcase, you would need to round up to the nearest whole number. Therefore, you need to borrow 43 bookcases.
So, the answer to (a) is: You need 43 bookcases.
b. Since each bookcase has 22 shelves and the last bookcase will have the remaining books after filling the previous bookcases, we first need to find out how many books are left after filling all the previous bookcases.
Number of bookcases: 43
Number of books on each shelf: 22
To find the total number of books displayed in the previous bookcases, multiply the number of bookcases by the number of shelves on each bookcase:
43 * 22 = 946
Now, subtract this total from the initial number of books (943) to find the number of books on each shelf of the last bookcase:
943 - 946 = -3
Since you cannot have a negative number of books on a shelf, we can conclude that the last bookcase is not completely filled. Therefore, the answer to (b) is: There are no books on each shelf of the last bookcase.