finding width and Height in word problem

Question

A bookcase is to have 4 shelves including the top

The width is to be 12 feet less than 4 times the height. Find the width and the height if the carpenter expects to use 24 feet of lumber to make it.
Width:____ feet
Height:____ feet

Answer 1

Let w = width and h = height. Then we have

 

w = 4*h - 12

 

and

 

4*w + 2*h = 24  (4 shelves and 2 sides).

 

Plug in the first equation into the second and solve for h:

 

4*(4*h - 12) + 2*h = 24

16*h - 48 + 2*h = 24

18*h = 72

h = 4

 

Plug that in the first equation to find w = 4*4 - 12 = 4

 

So width = height = 4 feet.