SOLUTION: this problem is not from my textbook and i really need help since word problems are not my strongest... The height of a rectangular box equals the length of an edge of a certain c

Question 60009: this problem is not from my textbook and i really need help since word problems are not my strongest...
The height of a rectangular box equals the length of an edge of a certain cube. The width of the box is 3 inches more than its height and the length of the box is 4 times its height. The volume of the box is 8 times the volume of the cube. Find the dimensions of the box and find the volume of the cube.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write a simple equation for each sentence.
:
"The height of a rectangular box equals the length of an edge of a certain cube"
Let x = height of the box, and x = dimension of the side of the cube
:
The width of the box is 3 inches more than its height
width = (x+3)
:
and the length of the box is 4 times its height.
Length = 4x
:
The volume of the box is 8 times the volume of the cube.
Length * Width * Height = 8 times the vol of the cube
4x * (x+3) * x = 8x^3
:
Find the dimensions of the box and find the volume of the cube.
If we find x we will know all.
:
4x * (x+3) * x = 8x^3
:
4x^2(x+3) = 8x^3
:
Divide both sides by 4x^2, resulting in:
(x + 3) = 2x
:
x - 2x = -3
:
-x = -3
:
x = +3 is the height and the cube side size
:
Length = 4(3) = 12
:
Width = (3 + 3) = 6
:
Vol of the cube: 3^3 = 27
:
Check to see if: 3*6*12 = 8*(3^3)

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