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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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