SOLUTION: Any help with the following word problem would be great. I just really need the help setting up the problem. A gardener has a rose garden that measures 30 feet by 20 feet. He

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Any help with the following word problem would be great. I just really need the help setting up the problem. A gardener has a rose garden that measures 30 feet by 20 feet. He       Log On


   

Question 320785: Any help with the following word problem would be great. I just really need the help setting up the problem.
A gardener has a rose garden that measures 30 feet by 20 feet. He wants to put a uniform border of pine bark around the outside of the garden. Find how wide the border should be if he has enough pine bark to cover 336 square feet.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width of the path be x feet.
The plan is to express the area of the garden with the border in terms of x, then subtract the area of just the garden. This will result in a quadratic equation in x which you solve by any of the appropriate methods available to you.
The area of the garden with border A%5B1%5D can be expressed as:
A%5B1%5D+=+%2830%2B2x%29%2820%2B2x%29 Simplify this to:
A%5B1%5D+=+4x%5E2%2B100x%2B600
The area of just the garden A%5B2%5D is:
A%5B2%5D+=+%2820%29%2A%2830%29
A%5B2%5D+=+600sq.ft.
Now subtract A%5B2%5D from A%5B1%5D.
A%5B1%5D+-+A%5B2%5D+=+4x%5E2%2B100x This is the area of the border of width x ft. which is given as 336 sq.ft., so...
4x%5E2%2B100x+=+336 Subtract 336 from both sides.
4x%5E2%2B100x-336+=+0 Simplify by factoring out a 4.
4%28x%5E2%2B25x-84%29+=+0 ...and from the zero product rule, you get that:
x%5E2%2B25x-84+=+0 You can solve this by factoring and you should get:
x+=+3 or x+=+-28
The width cannot be a negative quantity, so the width must be 3 feet.