SOLUTION: A bookcase is to have 4 shelves, the width is to be 8 feet less than 4 times the height. Find the width and the height if the carpenter expects to use 22 feet of lumber to make it.

Question 1145802: A bookcase is to have 4 shelves, the width is to be 8 feet less than 4 times the height. Find the width and the height if the carpenter expects to use 22 feet of lumber to make it.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
there are 4 shelves, which means there are 4 widths.
there are two heights (one on each end of the bookshelves that the bookshelves connect to).
since the total amount of lumber is 22 feet, then you get the equation:
4w + 2h = 22
w = width
h = height
since w = 4h-8, then replace w with that to get:
4*(4h-8) + 2h =22
simplify to get:
16h - 32 +2h = 22
add 32 to both sides of the equation and combine like terms to get:
18h = 54
solve for h to get h = 3
since w = 4h-8, then w = 12-8 = 4
you have w = 4 and h = 3.
4w = 16 and 2h = 6 for a total of 22 feet of lumber.
your solution is that the width = 4 feet and the height = 3 feet.

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