Question 109098: sasha works at the botanical gardens and is planning a new rectangular rose garden 20m by 30m. She plans to build a walkway, with a uniform width, all around the garden. Her budget is $6000 and she knows it will cost $10/m2 to construct the hallway. How wide can the walkway be?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangular rose garden 20m by 30m. a walkway, with a uniform width, all around the garden. budget is $6000 and it will cost $10/m2 to construct the walkway. How wide can the walkway be?
:
1st find the area of the walkway that will utilize the $6000 budget:
Area = 6000/10
A = 600 sq/m will be the area of the walkway
:
Let x = the width of the walkway:
:
Overall area: (30 + 2x) * (20 + 2x) = (600 + 100x + 4x^2);FOILed
:
30 * 20 = 600 sq/m = area of the garden only
:
The equation:
Overall area - garden area = walkway area
(4x^2 + 100x + 600) - 600 = 600
4x^2 + 100x - 600 = 0
Simplify, divide equation by 4
x^2 + 25x - 150 = 0
Factors to:
(x+30)(x-5) = 0
x = +5 meters is the solution we want here.
:
;
Check solution:
Overall area - garden area = walkway area
(40*30) - (30*20) =
1200 - 600 = 600
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