P = 2(L+W) (equation for the perimeter (P) in terms of length (L) and width (W))

L = W+77 (your relation between length and width)

P = 2((W+77)+W) = 2(2W+77) (substitute the second equation into the first, simplify)

230 = 2(2W+77) (substitute the value for perimeter)

115 = 2W+77 (divide both sides of the equation by 2)

38 = 2W (subtract 77 from both sides of the equation)

19 = W (divide both sides of the equation by 2)

L = (19) + 77 = 96 (use the second equation above to find L from W)

The length is 96 inches, and the width is 19 inches.

L = W+77 (your relation between length and width)

P = 2((W+77)+W) = 2(2W+77) (substitute the second equation into the first, simplify)

230 = 2(2W+77) (substitute the value for perimeter)

115 = 2W+77 (divide both sides of the equation by 2)

38 = 2W (subtract 77 from both sides of the equation)

19 = W (divide both sides of the equation by 2)

L = (19) + 77 = 96 (use the second equation above to find L from W)

The length is 96 inches, and the width is 19 inches.