I asked my teacher, and my teacher said it had 3 shelves..

Question

A bookcase is to be constructed. The height of the bookcase is 4 feet longer than the lenght of a shelf. If 20 feet of lumber is available for the entire unit (including the shelves, but NOT the back of the bookcase), find the length and height of the unit.

Could you please check my work:

p=20
l=2w+4
p=2l+2w
20=2(2w+4)+2w
20=4w+8+2w
20=6w+8
w=2

2(2)+4
4+4=8
L=8

It seems to me you have to specify how many shelves are required. Are you assuming two?
Why is l = 2w + 4?
Is l the length of the bookshelf?
The equation p = 20 = 2l + 2w does not allow any lumber for shelves.
The length of a shelf is w. If w = 2 and l = 8, the requirement that l = w + 4 is not met.

Answer 1

The length of a bookcase is to be 3 times the height. If 30feet of lumber is available for the entire unit, find the length and the height of the bookcase.