Question 119167
With this type of problem, always try to draw a picture and figure
out as much as you can just by looking at it and labeling parts
of it. The dimensions of the area including the walk are 16m x 22m
Let A = Area inluding walk
{{{A = 22*16}}}
{{{A = 352}}}
The area of the walk alone is 192 m2
From this the area of the pool is {{{P = 352 - 192}}}
{{{P = 160}}}m2
Looking at my drawing, {{{P = (22 - 2x)(16 - 2x)}}}
{{{160 = (22 - 2x)(16 - 2x)}}}
{{{160 = 352 - 32x - 44x + 4x^2}}}
{{{4x^2 - 76x + 352 = 160}}}
{{{4x^2 - 76x + 192 = 0}}}
{{{x^2 - 19x + 48 = 0}}}
I notice that {{{3*16 = 48}}} and {{{3 + 16 = 19}}} so, I
use these numbers as roots 
{{{(x - 3)(x - 16) = 0}}}
{{{x = 3}}} and {{{x = 16}}} solve the equation
I can discard {{{x = 16}}} because that's the size of
the width of the pool including the walk, so
The width of the walk is 3m answer
check answer
{{{160 = (22 - 2x)(16 - 2x)}}}
{{{160 = (22 - 2*3)(16 - 2*3)}}}
{{{160 = 16*10}}}
{{{160 = 160}}}
OK