walk area = area of large rectangle minus area of small rectangle (the small rectangle is the pool).
117 = large rectangle - 320
{add 320 to both sides}
437 = large rectangle area.
{note: walk is equal width.}
walk dimensions: the difference in dimension between large and small rectangle:
small rectangle = 16 * 20
let x be the difference (that is, the walk width)
large rectangle = (16 + x)(20 + x)
substitute:
437 = (16 + x)(20 + x)
437 = 320 + 36x + x^2
{subtract 437 from both sides, then
arrange for factoring}
x^2 + 36x - 117 = 0
{factor}
[first factor 117 to 3 * 3 * 13]
[look to arrange factors so there will be two, one negative, one positive (in view of the negative 117); and whose difference is 36]
[one possibility fits:]
(x + (3*13))(x - 3)
that is
(x + 39)(x - 3)
x = 3, -39
only one is viable:
x = 3
the walk width is 3 ft.
