SOLUTION: A gardener has a garden that is 20 feet wide and 100 feet long. She wants to have a stone border (along all 4 edges of the garden and inside of the garden) of uniform width. The st
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Question 163123: A gardener has a garden that is 20 feet wide and 100 feet long. She wants to have a stone border (along all 4 edges of the garden and inside of the garden) of uniform width. The stone border should use 100 square feet of crushed stone. How wide should the border be in inches?
You can put this solution on YOUR website! A gardener has a garden that is 20 feet wide and 100 feet long. She wants to
have a stone border (along all 4 edges of the garden and inside of the garden)
of uniform width. The stone border should use 100 square feet of crushed stone.
How wide should the border be in inches?
:
Let x = the width of the stone border
:
Find the area of the whole garden area:
20 * 100 = 2000 sq/ft
:
Find the area of the garden inside the stone border
(20-2x) * (100-2x) = 2000 - 240x + 4x^2 sq/ft
:
total area - inside stone border area = border area (100 sq/ft)
2000 - (2000 - 240x + 4x^2) = 100
:
removing brackets changes the signs
2000 - 2000 + 240x - 4x^2 - 100 = 0
:
-4x^2 + 240x - 100 = 0
:
Simplify equation, divide by -4, see if it will factor,
x^2 - 60x + 25 = 0:
No, so use the quadratic formula to solve this:
In this problem a=1; b=-60; c=25
Only one solution will make sense:
x =
x = .42 ft width of the stone border; about (.42 * 12 = 5 inches)
:
;
Check solution; find the area inside the border, subtract from 2000 sq/ft
(20-.84)*(100-.84) = 1899.9 ~ 1900 sq/ft
2000 - 1900 = 100 sq/ft as given
