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10 March, 19:12

Recall the shipping box scenario from the Introduction. As an employee of a sporting goods company, you need to order shipping boxes for bike helmets. Each helmet is packaged in a box that is n inches wide, n inches long, and 8 inches tall. The shipping box you order should accommodate the boxed helmets along with some packing material that will take up an extra 2 inches of space along the width and 4 inches of space along the length. The height of the shipping box should be the same as the helmet box. The volume of the shipping box needs to be 1,144 cubic inches. The equation that models the volume of the shipping box is 8 (n + 2) (n + 4) = 1,144.

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  1. 10 March, 19:56
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    The dimensions of the helmet box are as follows

    Width is 9 inches

    Length is 9 inches

    Height is 8 inches

    The dimensions of the shipping box ordered are as follows;

    Width is 11 inches

    Length is 13 inches

    Height is 8 inches

    Step-by-step explanation:

    8 (n + 2) (n + 4) = 1144

    8·n² + 48·n + 64 = 1144

    8·n² + 48·n - 1080 = 0

    8 * (n - 9) * (n + 15) = 0

    ∴ n = 9 or - 15 inches

    The dimensions of the helmet box are as follows

    Width = 9 in.

    Length = 9 in.

    Height = 8 in.

    The dimensions of the shipping box ordered are as follows;

    Width = 9 + 2 = 11 in.

    Length = 9 + 4 = 13 in.

    Height = 8 in.
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