Acarpenter is assigned a job of expanding a rectangular deck where the width is one-sixth the length. the length of the deck is to be expanded by 4 feet, and the width by 2feet. if the area of the new rectangle deck is 56 ft^2 larger than the area of the original deck, find the dimensions of the original deck

Let the original deck length be L
Let the original deck width be W

(L + 4)*(W + 2) = L*W + 56
LW + 2L + 4W + 8 = L*W + 56
2L + 4W + 8 = 56
2L + 4W = 48
L + 2W = 24
w = 1/6*L
L + 2*(1/6 L ) = 24
L + 1/3 L = 24
3L + L = 72
4L = 72
L = 18
W = 3

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