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Math Help - Rectangular Packing Box

  1. #1
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    Rectangular Packing Box

    A rectangular packing box, similar to a shoebox, without a lid, is 3 times as long as it is wide and half as high as it is long. Each square inch of the bottom of the box costs $0.008 to produce, while each square inch of any side costs $0.003 to produce.

    (A) Write an equation that represents the cost, c, of the box as a function of its width x.

    (B) Using the function written in part a, determine the dimensions of a box that would cost $0.69 to produce.

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  2. #2
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    Hello,

    so its width is x.
    We know that its length is 3 times as long as its width, meaning that its length is 3x.
    We know that its height is half as long as its length, meaning that its height is (3x)/2.

    If you view the box (I recommend you make a sketch), there is one bottom, rectangular, with its sides : length,width,length,width.
    So its area is (width * length) = 3x

    For two of the sides, the sides are : length,height,length,height.
    So each of their area is (length * height) = 9x/2

    For the last two sides, the sides are : width,height,width,height.
    So its area is (width * height) = 3x/2


    And finally, the cost will be ... ?


    For question b), solve for x in f(x)=0.69.
    This is not hard, just taking square roots
    If you struggle with that, let us know.
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