A rectangular 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=legnth times width=20 times 50=1000

the area of the deck is made up of 4 rectangles and 4 squares, the rectangles' areas come in pairs

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 2 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

therfor width of walkway=3ft