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Math Help - two cubes

  1. #1
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    two cubes

    The combined hieghts of two cubes are 11 metres and there combined volumes equal 407 cubic metres calculate the dimensions of each cube. need working out pleasee.
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  2. #2
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    Hello, ASSC!

    There is a very sneaky way to solve this one . . .


    The combined heights of two cubes are 11 metres
    and their combined volumes equal 407 cubic metres.
    Calculate the dimensions of each cube.

    Let x and y be the sides of the two cubes.

    Then we have:
    . . (1) . .x + y . = . 11
    . . (2) .x + y .= .407


    Cube (1): . . . . . . (x + y) .= .11

    . . . x + 3xy + 3xy + y .= .1331

    . . . (x + y) + 3xy(x + y) .= .1331
    . . . . . . . . . . . . . . .
    . . . . (407). . + . 3xy(11) . .= .1331


    This simplifies to: .xy .= .28 . . y .= .28/x

    Substitute into (1): . x + 28/x .= .11

    . . and we have: . x - 11x + 28 .= .0

    . . which factors: . (x - 4)(x - 7) .= .0

    . . and has roots: . x = 4, 7 . . y = 7, 4


    Therefore, the cubes have sides 4 metres and 7 metres.

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