Expert: Abe Mantell - 1/6/2010

Question
QUESTION: A bookshelf is to be constructed with 4 shelves.  The height is 3 feet more than the width.  

Amount of wood available- 30 feet.

Calculate dimensions of the bookcase.

Thanks for your assistance.

ANSWER: How do you count the shelves? Do the top and bottom count?  Only the bottom?
Or are there 4 *movable* shelves between the top and bottom ones that comprise
the frame?

It is important to know in order to answer the question.

Abe

---------- FOLLOW-UP ----------

QUESTION: The top and bottom count- none are movable.

Thanks again.

Answer
In that case...

Let x=the width of the bookshelf (in ft), so that x+3 = the height (in ft)

4 shelves requires 4x ft of wood, and 2 sides (for the height) require 2(x+3) ft.

Adding these we get: 4x + 2(x+3)= 30, neglecting the thickness of the wood.
==> 4x+2x+6=30 ==> 6x=24 ==> x=24/6 = 4 ft

Width = 4 ft, Height = 7 ft

Abe