Arectangular pool is 20 feet wide and 50 feet long. a deck used for sunning surrounds the pool. the deck is the same width all the way around the pool. the total area of the deck is 456 square feet. how wide is the walkway?

Deck=456
Area of pool= length times width=20 times 50=1000

The Area of the deck is made up of 4 rectangles and 4 squares, the rectangles Areas comes in pair.

Areas are 
Area of deck =2(20w)+4(w^2)+2(50w)d
456=2(20w)+4(w^2)+2(50w)
Distribute 
456=40w+4w^2+100w
Add Like Terms
456=4w^2+140w
Divide Everybody By 4
114=w^2+35w
Subtract 114 From Both Sides 
0=w^2+35w-114

Find What Two Numbers Multiply To Get 114 AND ADD TO GET  35 and FACTOR -3 and 38

0=(w-3)(w+38)
Set Each To Zero 
w-3=0
w=3 

w+38=0
w=-38
False since measures in real life cannot be negative therefore width of walkway =3ft
Hope I helped