A rectangular garden has dimensions of 18 feet by 12 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 504 square feet?

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Karina -Sometimes you need to "think outside the box" to find a math solution.  Here is an example how to do that!The picture below shows the layout of the garden.  The green inside rectangle is the garden that is 18 ft by 12 ft or a total of (18)(12) = 216 sq ft.The yellow area is the path around the garden. It has total area equal to 504 sq ft.So here is the trick ... area of the garden PLUS the pathway is 216 + 504 = 720 sq ft.  But, this area is also equal to the area of the large rectangle with dimensions:(18 + 2w) by (12 + 2w)Now just set these two areas equal to each other and solve for w:(18 + 2w) (12 + 2w) = 720 sq ft4w^2 + 60w +216 = 7204w^2 +60w -504 = 0w^2 +15w -126 = 0(w-6)(w+21) = 0So, w = 6 ft = width of the path.Hope that helps