Question 1194005
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A rectangular garden is 4 m by 12 m. It is to be surrounded by a walkway of uniform width.
Write a relation in standard form for the total are of the garden and walkway
I figured that out to be A=4x^2 +32x+48
This is the part I don't get, Stones for the walkway cost $9/m^2 
If the to total cost of the walkway cannot exceed $1200, what is the maximum allowable width of the walkway? 
Thank you
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<pre>
Let x be the width of the walkway, in meters.


The total area of the garden surrounded by the walkway is

    (4+2x)*(12+2x) = 4x^2 + 32x + 48 square meters.


It is what you get in your post.


To get the area of the walkway, you should subtract 4*12 = 48 square meters from it, which is the area of the garden.

You will get then  

    (4x^2 + 32x + 48) - 48 = 4x^2 + 3x  square meters, the area of the walkway.


The cost of the stone is  9*(4x^2+3x) = 36x^2 + 27x  dollars.


It should be less than or equal to 1200  dollars

     36x^2 + 27x <= 1200,

or

    12x^2 + 9x <= 400

    12x^2 + 9x - 400 <= 0.


The roots of the quadratic function on the left are 5.41 and -6.16  (approximately), obtained with the quadratic formula.


So, the maximum walkway width is about 5.41 meter.    <U>ANSWER</U>
</pre>

Solved.