college algebra word problem “landscaping project”

Question

As part of the landscaping project, you put in the flower bed measuring 10’ x 20’. To finish off the project, you are putting in a uniform border of Pinebark around  The outside of the rectangular garden. You have enough Pinebark to cover 304 ft.². How wide should the border be? 

Answer 1

Since it's a uniform border, let x = the width of the border

 

The length of the border is 20 + x + x (since it has a border on both sides) or 20+2x

The width is 10+x+x or 10+2x

 

We have enough to cover 304 sq ft, so the area to cover is the area with the border minus the area of the flower bed

 

Area with border = (20+2x)(10+2x)

Area of flower bed = 10x20 = 200

Area of border = area with border - area of flower bed = (20+2x)(10+2x) - 200

 

(20+2x)(10+2x)-200 = 304

200+40x+20x+4x²-200 = 304

 

4x²+60x=304

 

4x²+60x-304 = 0

 

You can factor out a 4

 

x²+15x-76 = 0

 

Now you can solve for x using quadratic equation or factoring (it can be factored)

 

 

Answer 2

 

2*10*w + 2*20*w + 4*w^2 = 304

 

4w^2 + 60w = 304

 

4w^2 + 60w - 304 = 0

 

w^2 + 15w - 76 = 0

 

( w   +   19 )( w   -   4  ) = 0

 

w+19=0 results in negative measures.

 

w=4