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17 August, 01:25

Andre is preparing for the school play and needs to paint the rectangular cardboard castle backdrop that measures LaTeX: 14/frac{1}{4}14 1 4feet by 6 feet. If one bottle of paint covers an area of 40 square feet, how many bottles of paint does Andre need for his backdrop? Enter your numerical answer with no label.

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  1. 17 August, 01:42
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    2.1375 bottles of paint

    Step-by-step explanation:

    cardboard length = 14 1/4 ft, which is equivalent to (4*14 + 1) / 4 = 57/4 ft

    cardboard width = 6 ft

    Rectangular cardboard area = length * width = 57/4 * 6 = (57*6) / 4 = 342/4 ft², which can be simplified dividing numerator and denominator by 2: 171/2 ft²

    If 1 bottle of paint covers an area of 40 square feet, then to paint 171/2 square feet the following proportion must be satisfied:

    1 bottle of paint / 40 square feet = x bottles of paint / (171/2) square feet

    x = (1/40) * (171/2) = (1*171) / (40*2) = 171/80 or (160 + 11) / 80 = 160/80 + 11/80 = 2 11/80 or 2.1375 bottles of paint
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