SOLUTION: A landscaper, who just completed a rectangular flower garden measuring 6 feet by 10 feet, orders 1 cubic yard of premixed cement, all of which is to be used to create a border of
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Question 1199114: A landscaper, who just completed a rectangular flower garden measuring 6 feet by 10 feet, orders 1 cubic yard of premixed cement, all of which is to be used to create a border of uniform width around the garden. If the border is to have a depth of 3 inches, how wide will the border be?
Without going into too much detail, in this website I found that someone answered the question by coming up with the following equation:
(2x + 6) (2x + 10) = 168
Let x = width of the border.
My question is:
Where did 168 come from?
Thanks. Answer by ikleyn(52803) (Show Source):
Below I will explain you on how to set up an equation to this problem.
The area of the large rectangle (the garden plus the walkway around the garden) is (2x+6)*(2x+10) square feet.
The area of the garden itself is 6*10 = 60 square feet.
The area of the walkway is the difference (2x+6)*(2x+10) - 60 square feet.
The volume of 1 cubic yards, converted to cubic feet is = 27 cubic feet.
When laid on the level ground with the thickness of 3 inches = of a foot,
1 cubic yard covers the area = 27*4 = 108 square feet.
So, 108 square feet is the area, which should be in the right side of this equation
(2x+6)*(2x+10) - 60 = 108.
Both sides of this equation represent the same quantity: the area of the walkway.
It leads to the equation
(2x +6)*(2x+10) = 168.
It is exactly the equation you asked about.
In the original solution under this link
https://www.algebra.com/algebra/homework/word/geometry/Geometry_Word_Problems.faq.question.1126574.html
the tutor obtained the same equation in another way (as the area of the large rectangle "the garden + the walkway").
After completing the setup, the solution goes on the way
shown by the tutor under the cited link.
