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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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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. ANSWER
Solved.