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

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?

Answer by ankor@dixie-net.com(22740) (Show Source): 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

RELATED QUESTIONS
a gardener has a garden that is 20 feet wide and 100 feet long. She wants to have a stone (answered by josmiceli)

Gardening. A gardener has planted a rectangular garden that measures 8 feet by 5 feet. He (answered by ankor@dixie-net.com)

Lisa has a rectangular garden which is 23 feet long and 15 feet wide. She has 240 square... (answered by Alan3354)

The rectangle is 33 feet long and 25 feet wide if the gardener wants to build a fence... (answered by ikleyn)

Suzanne has a rectangular garden which is 49 feet long and 41 feet wide. She has 581... (answered by ankor@dixie-net.com)

A gardener has a 30 foot by 20 foot rectangular plot of ground. She wants to build a... (answered by stanbon,josmiceli)

A gardener has 73 feet of fencing to be used to enclose a rectangular garden that has a... (answered by ikleyn)

Good day! kindly help me with this word problem. Thanks! A park department gardener... (answered by ankor@dixie-net.com)

The rectangle is 22ft long and 17ft wide. If the gardener wants to build a fence around... (answered by ewatrrr)