SOLUTION: Please help me with this word problem: A large plywood box has a volume of 72 ft3. Its length is 9 ft greater than its height, and its width is 1 ft less than its height. What are

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Question 708445: Please help me with this word problem: A large plywood box has a volume of 72 ft3. Its length is 9 ft greater than its height, and its width is 1 ft less than its height. What are the dimensions of the box?
What does x equal?
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A large plywood box has a volume of 72 ft3.
Its length is 9 ft greater than its height, and its width is 1 ft less than its height.
What are the dimensions of the box?
:
let x = the height
:
"Its length is 9 ft greater than its height,"
L = (x+9)
:
its width is 1 ft less than its height."
W = (x-1)
:
L * W * H = 72
therefore
(x+9)*(x-1)*x = 72
FOIL
(x^2 - x + 9x -9 )*x = 72
Which is
x^3 + 8x^2 - 9x - 72 = 0
We can group factor here
x^2(x+8) - 9(x+8) = 0
Factor out (x+8)
(x+8)(x^2-9) = 0
three solutions
x = -8
and
x^2 = 9
x = +/-
x = +3
and
x = -3
:
IN the real world of boxes only the positive solution will be valid
x = 3
then the box dimensions:
3 + 9 = 12 is the length
3 - 1 = 2 is the width
3 = the height
:
See if that flies: 12 * 2 * 3 = 72