Question 1176533: franks pool measures 20 feet by 40 feet. frank has decided to surround his pool with a deck made from new paving stones .if the deck has a unifrom width around the entire pool , and the area of the combined pool and deck is 1500 square feet then what is the width of his deck? only is a algebracic soultion
Found 2 solutions by Solver92311, ankor@dixie-net.com:
Answer by Solver92311(821)   (Show Source):
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! franks pool measures 20 feet by 40 feet.
frank has decided to surround his pool with a deck made from new paving stones. If the deck has a uniform width around the entire pool, and the area of the combined pool and deck is 1500 square feet, then what is the width of his deck?
:
let w = the width of the deck
Then the overall dimensions of the deck and pool:
(2w+20) by(2d+40)
the overall area:
(2w+20)*(2w+40) = 1500
FOIL
4w^2 + 80w + 40w + 800 = 1500
Combine to form a quadratic equation
4w^2 + 120w + 800 - 1500 = 0
4w^2 + 120w - 700 = 0
simplify, divide by 4
w^2 + 30w - 175 = 0
you can use the quadratic formula, a=1, b=30, c=-175, but this will factor to
(w - 5)(c + 35) = 0
the positive solution is reasonable
w = 5 feet is the width of the deck
:
See if that checks out, add 10 ft to the pool dimensions
30 * 50 = 1500
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