Algebra

Sabrinia is building a rectangular raised flower bed. The boards on the two shorter sides are 6 inches thick, and the boards on the two longer sides are 4 inches thick. Sabrina wants the outer length of her bed to be 4 times its height and the outer width to be 2 times its height. She also wants the boards to rise 4 inches above the level of the soil in the bed. What should the outer dimesnions of the bed be if she wants it to hold 3136 cubic inches of soil?

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  1. If the boards are h inches high, then the soil is (h-4)" deep.

    If the outside dimensions are x and y, with x<y,

    x=2h
    y=4h

    So, the inner dimensions are (x-8) and (y-12), and using the given volume,

    (h-4)(x-8)(y-12) = 3136
    h(2h-8)(4h-12) = 3136
    h = 11 inches.

    Check:
    The outer width is 22
    The outer length is 44
    The inner width is 14
    The inner length is 32
    The depth is 7

    14*32*7 = 3136

    Nice problem! At first I thought not enough information was provided.

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