Thread: Polynomial Story Problem

As part of a landscaping project, you put in a flower bed measuring 10 feet by 12 feet. You plan to surround the bed with a uniform border of low-growing plants.

Write a polynomial that describes the area of the uniform border that surrounds the bed. Explain what you did and why.

The low-growing plants surrounding the flower bed require 1 sq. foot each when mature. If you have 168 of these plants, how wide a strip around the bed should you prepare the border? Explain what you did and why.

If someone can help me set up the problem, I can figure out how to solve it.

Hello, mjfaris!

Did you make a sketch?

You put in a flower bed measuring 10 feet by 12 feet.
You plan to surround the bed with a uniform border of low-growing plants.

(a) Write a polynomial that describes the area of the uniform border that surrounds the bed.
Explain what you did and why.

(b) The plants in the border require 1 ft² each when mature.
If you have 168 of these plants, how wide should the border be?

Code:

      : x :    12    : x :
    - * - - -  - - - - - *
    x |                  |
    - |   * - -  - - *   |
      |   |    12    |   |
   10 |   |10        |   | 2x+10
      |   |          |   |
    - |   * - - -  - *   |
    x |                  |
    - * - - - - - -  - - *
             2x+12

The inner bed is 10-by-12 feet.
. . Its area is: . ft².

The border is feet wide.

The length of the entire garden is: feet.
The width of the entire garden is: feet.
. . Its area is: . ft².




So, we have: .


Can you finish it now?

Thank you so much!

I understand how you got A. But, for the life of me I can not figure out B. This is also a problem for my algebra homework. Please help me!