Charlie has a collection of books that he wishes to display in a narrow bookcase with shelves of width 56cm. The thickest books are no more than 16cm wide and, when placed side by side, the entire collection takes up 2.4m. Find, with justification, the minimum number of shelves required to guarantee that all of the books can be displayed in the bookcase.

5 shelves

Step-by-step explanation:

Given the following :

Width of shelves = 56cm

Maximum thickness of books = 16cm

When placed side-by-side, the entire collection of books takes up 2.4m

Minimum number of shelves required to guarantee that all of the books can be displayed in the book case.

Entire book collection = 2.4m = (2.4 × 100) = 240cm

Width of shelf = 56cm

In other to guarantee that the bookshelf contains all the books, we can assume that the each book is of maximum width, 16cm

Hence, maximum number of books each shelf can hold with guarantee

Width of shelf / max. Width of book

= 56cm / 16cm = 3.5

Hence, a shelf can hold 3 books with full guarantee.

If books are all 16cm thick, then the number of books ;

240 cm / 16 cm = 15 books

If one shelf can hold 3 books, then,

15/3 = 5 shelves are required to hold the books with maximum guarantee.

or