Question

A shipping service restricts the dimensions of theboxes it will ship for a certain type of service.The restriction states that for boxes shaped likerectangular prisms, the sum of the perimeter of thebase of the box and the height of the box cannotexceed 130 inches. The perimeter of the base isdetermined using the width and length of the box.If a box has a height of 60 inches and its length is2.5 times the width, which inequality shows theallowable width x, in inches, of the box?A) 0 < x ≤ 10B) 0 < x ≤ 11(2/3)C) 0 < x ≤ 17(1/2)D) 0 < x ≤ 20

Answers

  1. The inequality which allow able for width x is 0 ≤ x ≤ 10.
    According to the given question.
    The sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches.
    Width
    Let the length, and height of the box be l, and h respectively.
    Therefore,
    The perimeter of the base of box = 2(width + l) = 2(x + l)
    Also, it is given that
    l = 2.5x
    So,
    perimeter of the base = 2(x + 2.5x) = 2(3.5x)
    Now, according to the given condition.
    The sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches.So, the inequlaity which represent this scenario is
    2(3.5x) + 60 ≤ 130
    ⇒ 7x ≤ 130-60
    ⇒ 7x ≤ 70
    ⇒ x ≤ 10  
    Also, x is the width of the box, so it must have some measure and cant be negative therefore
    0 ≤ x ≤ 10.
    Hence, the inequality which allow able for width x is 0 ≤ x ≤ 10.
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