Question

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

The width is to be 5 feet less than 3 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:

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.