High School

Allen is putting up a rectangular fence in his backyard. He is also putting two circular flower beds inside the fence.

- The length of the fence will be 25 feet.
- The radii of the flower beds must be at least 2 feet less than the width of the fence.
- Allen can spend no more than $400 on the fence and flower bed materials.
- The cost of the fence is $2.50 per linear foot.
- The cost of the material for the flower beds is $1.60 per square foot.

If \( y \) represents the width of the fence and \( x \) represents the radii of the flower beds, which system of inequalities can be used to determine the width of the fence and the radii of the flower beds?

Answer :

Final answer:

To determine the systems of inequalities, assign variables to the unknowns and consider the given information. The systems of inequalities are y = 25, x = y - 2, and 2.50y + 1.60(πx^2) ≤ 400.

Explanation:

To determine the systems of inequalities that can be used to determine the length and width of the fence and the radii of the flower beds, we need to consider the given information. Let's start by assigning variables to the unknowns.

Let y represent the width of the fence and x represent the radii of the flower beds.

Based on the given information, we can create the following systems of inequalities:

System of Inequalities:

  1. y = 25 (Width of the fence is 25 feet)
  2. x = y - 2 (Radii of the flower beds is at least 2 feet less than the width of the fence)
  3. 2.50y + 1.60(πx^2) ≤ 400 (Cost of fence and flower bed materials is no more than $400)

Learn more about Systems of Inequalities here:

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