A carpenter 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

You should check this answer to see if it is right (it does check)

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