SOLUTION: The Monahan’s garden is 20 feet by 30 feet. They wish to lay a uniform border of pine bark around the garden. How large a strip should they lay if they only have enough bark to c

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Question 275084: The Monahan’s garden is 20 feet by 30 feet. They wish to lay a uniform border of pine bark around the garden. How large a strip should they lay if they only have enough bark to cover 360 square feet?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The Monahan’s garden is 20 feet by 30 feet.
They wish to lay a uniform border of pine bark around the garden.
How large a strip should they lay if they only have enough bark to cover 360 square feet?
:
let x = the width of the border
:
Find the area of the garden 20 * 30 = 600 sq/ft
then
The total area, border & garden: 360 + 600 = 960 sq/ft
:
the overall dimensions of border and garden: (2x+20) by 2x+30)
:
The overall area:
(2x+20) * (2x+30) = 960
FOIL
4x^2 + 60x + 40x + 600 = 960
:
4x^2 + 100x + 600 - 960 = 0
:
4x^2 + 100x - 360 = 0; our old friend, the quadratic equation
Simplify,divide by 4
x^2 + 25x - 90 = 0
Unfortunately this will not factor, Use the quadratic equation
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=1; b=25; c=-90
x+=+%28-25+%2B-+sqrt%2825%5E2-4%2A1%2A-90+%29%29%2F%282%2A1%29+
:
x+=+%28-25+%2B-+sqrt%28625+-+%28-360%29%29%29%2F2+
:
x+=+%28-25+%2B-+sqrt%28625+%2B+360%29%29%2F2+
:
x+=+%28-25+%2B-+sqrt%28985%29%29%2F2+
the positive solution
s+=+%28-25+%2B+31.38%29%2F2+
:
x = 6.38%2F2
x = 3.19 ft is the width of the border
:
:
Check solution on calc using 3.2 for the width
26.4 * 36.4 = 961 ~ 960;
Subtract the area of the garden: 960 - 600 = 360, the area of the border