Question 780474: I have a word problem that I need to solve for school and I don't know how to set this up, I'm guessing it's using the quadratic equation because that was our topic in class today but I don't know how this one goes:
Frank is decorating a porch the measures 10 yards by 20 yards. He wants to paint a uniform border around the sides and leave 96 square yards in the middle of the floor for a faux rug painting. How wide should he paint the border?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
So you don't know the width of the border. That makes the width of the border a good candidate to be  , right? Then the width of the area in the center that is supposed to measure 96 square yards has to be the 10 yards that is the width of the porch minus yards on each side, so  . Likewise, the length of the center part has to be  . The area of a rectangle is the length times the width, so:
(20\ -\ 2x)\ =\ 96)
Multiply the two binomials, collect all terms in the LHS so that the LHS is equal to zero, and then solve by any convenient means. Given your lesson for today on the quadratic formula, the need for such is a reasonably good guess. However, once you calculate the discriminant, you should see that the radicand is a perfect square. Hence the quadratic is indeed factorable. You will get two positive roots of this equation but one of them is absurd, so discard it.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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