The perimeter of a rectangle is 86 units. The length is 7 more than 5 times the width. Find the length.
Perimeter = L + L + W + W = 2L + 2W
L= 5W + 7 (given)
or (L-7)/5 = W
2L + 2W = 86 (substitute in W = (l-7)/5)
2L + 2 ( L-7)/5 = 86 (multiply both sides by 5)
10L + 2L - 14 = 430 (simplify)
12L = 444 (divide both sides by 12)
L = 37 W = 6