A bookcase is to have 4 shelves including the top The width is to be 2 feet less than 2 times the height Find the width and the height if the carpenter expects to use 22 feet of lumber to make it.

The width of the bookcase = 4ft

The height of the bookcase = 3ft

Step-by-step explanation:

Let H be the height of the bookcase

Let W be the width of the bookcase

W = 2H - 2ft

A bookcase of 4 shelves will have four widths and 2 heights

2H + 4W = 22ft

Put W = 2H - 2ft into the equation above

2H + 4 (2H - 2ft) = 22ft

2H + 8H - 8ft = 22ft

10H - 8ft = 22ft

Collect like terms

10H = 22ft + 8ft

10H = 30ft

H = (30/10) ft

H = 3ft

The bookcase has a height of 3ft each

Put H = 3ft into the equation

2H + 4W = 22ft

2 (3) + 4W = 22ft

6ft + 4W = 22fr

4W = 22ft - 6ft

4W = 16ft

W = (16/4) ft

W = 4ft

The width of the bookcase is 4ft each