SOLUTION: Gardening. A gardener has planted a rectangular garden that measures 8 feet by 5 feet. He has ordered 1 cubic yard (27 feet) of stones for a border along the outside of the garden.

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Question 210186: Gardening. A gardener has planted a rectangular garden that measures 8 feet by 5 feet. He has ordered 1 cubic yard (27 feet) of stones for a border along the outside of the garden. If the border needs to be 4 inches deep and he wants to use all of the stones, how wide should the border be?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A gardener has planted a rectangular garden that measures 8 feet by 5 feet.
He has ordered 1 cubic yard (27 feet) of stones for a border along the outside of the garden.
If the border needs to be 4 inches deep and he wants to use all of the stones,
how wide should the border be?
:
Find the area of the border using 27 cu/ft of material
4 inches = 1%2F3 ft
27 ft divided by 1%2F3 = 81 sq/ft
:
Area of the garden: 8 * 5 = 40 sq/ft
:
Let x = width of the border
:
Overall area
(2x+8)*(2x+5) = 4x^2 + 10x + 16x + 40 = 4x^2 + 26x + 40 sq/ft
:
Overall area - garden area = border area
(4x^2 + 26x + 40) - 40 = 81
:
4x^2 + 26x - 81 = 0
:
Use the quadratic formula: a=4; b=26; c=-81
:
You should get a positive solution: x = 2.30 ft, is the width of the border