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.

Group of answer choices

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