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Question 189723: A box has dimensions that have consecutive numbers for its length, width and height, the height having the smallest of the three dimensions. If the length and width are increased by 2 cm and the height is doubled, the volume now becomes 192 cm3 greater than the original box. What are the dimensions of the original box?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A box has dimensions that have consecutive numbers for its length, width and height, the height having the smallest of the three dimensions. If the length and width are increased by 2 cm and the height is doubled, the volume now becomes 192 cm3 greater than the original box. What are the dimensions of the original box?
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Let the dimensions be "x-1", x, and "x+1"
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Original dimensions:
height = x-1
length = x
width = x+1
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Equation:
Original volume is (x-1)*x*(x+1) = x(x^2-1) = x^3-x
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New dimensions:
height = 2x-2
length = x+2
width = x+3
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Equation:
new volumn - old volumn = 19 2cm^3
2(x-1)(x+2)(x+3) - (x^3-x) = 192
x = 4
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Answer:
height = x-1 = 3
length = x = 4
width = x+1 = 5
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Cheers,
Stan H.
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