Beverly L. answered • 04/12/15

Need Math, Chemistry, or Economics help? BA ECON/CHEM, MS ECON.

The total area of the deck (456 sq ft) is the length x width of the deck and the pool MINUS the length x width of the pool. We are told the deck is the same width all around the pool, let's call this number

*y.*We can now define the length and width of the pool plus the deck aslength= 50 + y

width= 20 +y

Area of the pool and the deck= (50+y)*(20+y)=1000+50y+20y+y^2= y^2 + 70y +1000

We also know that the length of the pool is 50 ft and the width of the pool is 20 ft

Therefore, we know the area of the pool:

Area= 50* 20 = 1000

We know the total area of the deck is the length x width of the deck and the pool MINUS the length x width of the pool:

456 sq ft = [y^2 + 70y + 1000] - 1000

456 = y^2 + 70y

Rearranging the equation, we get:

y^2 + 70y - 456= 0

(y-6)(y+76)=0

y= 6 or y=-76

Since we know that length cannot be a negative number, y must be 6. The walkway is therefore 6ft wide.