Math Help quadratics?

Bob works at a garden 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/m^2 to construct the walkway. How wide can the walkway be?

Math Help quadratics?
First off: Bob?



Back to the problem:

Since it is a 20x30 garden the walkway dimensions is greater than 20x30 and on a sidenote lets say the width of the walkway is x.



Two find the area, just subtract the walkway+garden area by the garden area.



The walkway+garden is: (2x+20)*(2x+30)-(600)



Why 2x? That's b/c the width is applied on both sides of the length and width of the rect.



Now FOIL it out subtract the 600, and multiply it by 10.



You should get:



6000=(some quadratic)



Now just subtract the 6000 and solve for x.
Reply:If the walkway has a width w then it will have a length of

2*(30+w) + 2*(20+w) = 100 + 4w



So the area of the walkway = length*width

= (100+4w)*w = 100w + 4w^2



The price of the walkway is (100w+4w^2)10 = 6000



40w^2 + 1000w - 6000 = 0

w^2 + 25w - 150 = 0

(w - 5)(w + 30) = 0



So the width must be 5 meters