SOLUTION: i have a question on a story problem? a rectangular swimming pool is surrounded by a cement walk of uniforn width.let x represent this width.. The outer dimensions of the wark a

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Question 119167This question is from textbook
: i have a question on a story problem?
a rectangular swimming pool is surrounded by a cement walk of uniforn width.let x represent this width..
The outer dimensions of the wark are 16m by 22m and the area of the walk alone is 192m^2. What is the width of the walk?
16x + 22y=192
then what?or isnt that even right
This question is from textbook

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
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%2A16
A+=+352
The area of the walk alone is 192 m2
From this the area of the pool is P+=+352+-+192
P+=+160m2
Looking at my drawing, P+=+%2822+-+2x%29%2816+-+2x%29
160+=+%2822+-+2x%29%2816+-+2x%29
160+=+352+-+32x+-+44x+%2B+4x%5E2
4x%5E2+-+76x+%2B+352+=+160
4x%5E2+-+76x+%2B+192+=+0
x%5E2+-+19x+%2B+48+=+0
I notice that 3%2A16+=+48 and 3+%2B+16+=+19 so, I
use these numbers as roots
%28x+-+3%29%28x+-+16%29+=+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+=+%2822+-+2x%29%2816+-+2x%29
160+=+%2822+-+2%2A3%29%2816+-+2%2A3%29
160+=+16%2A10
160+=+160
OK