Question 447437
A gardener has a rose garden that measures 30 feet by 20 feet. 
He wants to put a uniform border of pine bark around the outside of the garden. Let x be the width of the border in feet. 
Write an expression for the total area of the border in terms of the width x.
I came up with 4x^2 + 100x as my answer. Correct?
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Draw the picture:
You have a rectangle inside a rectangle.
The area of the larger rectangle is (30+2x)(20+2x)
The area of the inside rectangle is 30*20
So the area of the border is (30+2x)(20+2x)-30*20 = 4x^2+100x sq. ft.
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Find out how wide the border should be if he has enough pine bark to cover 336 square feet. 
I came up with 3 feet as my answer. Correct?
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Solve 4x^2+100x = 336
x^2+25x-84 = 0
(x-3)(x+28) = 0
Positive solution:
x = 3 ft.
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If the border needs to be covered to a depth of 3 inches and pine bark costs $29 per cubic yard, what will the material cost to lay the pine bark border? Assume that you must purchase a whole number of cubic yards and not a fraction of a cubic yard.
Volume = (area)(depth) = 336 sq.ft * (0.25 ft) = 84 cu. ft 
84 cu ft = 84/27 = 3.111 cu yrd
Price = 3.1111*$29 = $90.22
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Also, now assume you can actually buy as much or as little bark as you need to cover the border area, that is, the vendor will sell even a small fraction of a cubic yard if you want. Write an expression for the cost in dollars as a function of the width x, of the border in feet. Assume again that the border is to be covered to a depth of 3 inches and that pine bark costs $29 per cubic yard.
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Volume = (area)(depth)
Volume = [(4x^2+100x)(1/4)]/27  = (27/4)(4x^2+100x) cu. yds
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Cost = (29*27/4)(4x^2-100x) = 195.75*4(x^2-25x) = 783(x^2-25x) dollars
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Cheers,
Stan H.