A bookcase is to have 4 shelves including the top

Question

A bookcase is to have 4 shelves including the top as pictured below.

The width is to be 11 feet less than 3 times the height. Find the width and the height if the carpenter expects to use 26 feet of lumber to make it.

Width:  feet

Height:  feet

Answer 1

w = 3h-11

4w + 2h = 26

2w + h = 13

h=13-2w

w = 3(13-2w) -11 = 39-6w -11 = 28-6w

7w = 28

w = 28/7 = 4 feet wide

h= 13-8 = 5 feet high