You are putting a stone borderof uniform width around a rectangular garden that measures 6 yards by 15 yards. You only have enough stone to cover 100 square yards. How wide should the border be? Solve using the 5 step process.

Question

You are putting a stone borderof uniform width around a rectangular garden that measures 6 yards by 15 yards. You only have enough stone to cover 100 square yards. How wide should the border be? Solve using the 5 step process.

Answer 1

Area of garden NOT covered with stone border

= (15-2x)(6-2x)

so
(15)(6) - (15-2x)(6-2x) = 100

solve this resulting equation for x

Answer 2

To solve this problem using the 5 step process, we need to follow these steps:

Step 1: Understand the problem.
We have a rectangular garden measuring 6 yards by 15 yards, and we want to add a stone border of uniform width around it. We are given that we only have enough stone to cover 100 square yards. We need to find out how wide the border should be.

Step 2: Plan a solution.
To find out how wide the border should be, we can subtract the area of the garden from the total area covered by the stone to find the area of the border. Then, we can calculate the width of the border by dividing the area of the border by the length of the perimeter of the garden.

Step 3: Execute the plan.
Let's calculate the area of the garden first:
Area of the garden = Length × Width = 6 yards × 15 yards = 90 square yards

Now, we can calculate the area of the border:
Area of the border = Total area covered by the stone - Area of the garden = 100 square yards - 90 square yards = 10 square yards

Next, we need to find the perimeter of the garden:
Perimeter of the garden = 2 × (Length + Width) = 2 × (6 yards + 15 yards) = 42 yards

Finally, we can find the width of the border by dividing the area of the border by the perimeter of the garden:
Width of the border = Area of the border ÷ Perimeter of the garden = 10 square yards ÷ 42 yards ≈ 0.2381 yards (rounded to 4 decimal places) or approximately 8.57 inches.

Step 4: Evaluate the solution.
The width of the border comes out to be approximately 0.2381 yards or 8.57 inches. Since the problem doesn't specify the desired units, we'll assume you want the answer in yards.

Step 5: Provide the answer.
Therefore, the border should be approximately 0.2381 yards wide.