A carpenter is assigned the job of expanding a rectangular deck where the length is four times the width. The width of the deck is to be expanded by 3 feet and the length is to be expanded by the new width. If the area of the new rectangular deck is 124 ft larger than the area of the original deck, find the dimensions of the original deck.
Original deck :
width --- x ft
length -- 4x ft
new deck:
width = x+3 ft
length = 4x + (x+3) = 5x+3
(x+3)(5x+3) - x(4x) = 124
5x^2 + 18x + 9 - 4x^2 - 124 = 0
x^2 + 18x - 115 = 0
solve for x, (it factors or just use the formula)