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17 June, 11:56

A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. The restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches. The perimeter of the base is determined using the width and length of the box. If a box has a height of 60 inches and its length is 2.5 times the width, which inequality shows the allowable width in inches, of the box?

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  1. 17 June, 12:02
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    w = < 70

    (width is less or equal to 70 inches)

    Step-by-step explanation:

    Let l = length, w = width, h = height

    Restrictions given in this question:

    'sum of perimeter of the base and the height cannot exceed 130 inches'

    perimeter of the base is 2 width and 2 length of the box

    perimeter = 2w + 2l

    Therefore, inequality involves here is

    2w + 2l + h = < 130

    (Note that = < here means less or equal)

    Then a new condition given with

    height, h = 60 in

    and length is 2.5 times the width

    l = 2.5w

    Substitute this new condition into the equation will give us the following:

    2w + 2 (2.5w) + 60 = < 130

    2w + 5w + 60 = < 130

    7w + 60 = < 130

    7w = < 130-60

    7w = < 70

    w = < 10
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