Question

A bookcase with 4 shelves and the width is to be 7 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

Answer 1

Answer is
Height = 5 ft and Width = 3 ft

Step by step

H=height; W=width

Your equations are labeled A and B.
(A). W=2H-7
(B). 2H+4W=22
(2 height boards, 4 width boards = 22ft total)

Substitute equation A value in place of W.

2H+4(2H-7ft)=22ft
Distributive multiply parentheses

2H+8H-28ft=22ft

Add 28 ft to each side to isolate H

2H + 8H -28 + 28 = 22 + 28

10H=50ft

Divide both sides by 10 to solve for H

H=5 ft
ANSWER 1: The bookshelf is 5 feet high.

Now we substitute the H value into equation A to solve for W

W=2H-7ft

W = 2(5ft)-7ft

W = 10ft-7ft

W=3ft ANSWER 2: the bookshelf is 3 feet wide.

CHecK your work by substituting your H and W values into equation B

2H+4W=22ft

2(5ft)+4(3ft)=22ft

10ft+12ft=22ft

22ft=22ft

Problem solved!