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 deck around the pool? Show your work
A)2 feet
B)3feet
C)4 feet
D) 5 feet
Let x be the width of the deck around the pool.
The area of the entire rectangle (including the pool and the deck) is (20+2x)(50+2x) square feet.
The area of just the pool is 20*50 = 1000 square feet.
So, the area of the deck is (20+2x)(50+2x) - 1000 square feet.
Given that the total area of the deck is 456 square feet, we have:
(20+2x)(50+2x) - 1000 = 456
1000 + 40x + 100x + 4x^2 - 1000 = 456
40x + 100x + 4x^2 = 456
4x^2 + 140x - 456 = 0
x^2 + 35x - 114 = 0
(x + 38)(x - 3) = 0
x = 3 or x = - 38
Since the width of the deck cannot be negative, x = 3 feet.
Therefore, the width of the deck around the pool is 3 feet.
The correct answer is B) 3 feet.