SOLUTION: A rectangular garden is surrounded by a walk of uniform width. The area of the garden is 180 square yards. If the dimensions of the garden plus the walk are 16 yards by 24 yards,

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A rectangular garden is surrounded by a walk of uniform width. The area of the garden is 180 square yards. If the dimensions of the garden plus the walk are 16 yards by 24 yards,       Log On


   

Question 836646: A rectangular garden is surrounded by a walk of uniform width. The area of the garden is 180 square yards. If the dimensions of the garden plus the walk are 16 yards by 24 yards, find the width of the walk.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Area of the walkway plus area of the garden equals total area of walkway and garden.

Walkway+%2B+Garden+=+CombinedWalkwayAndGarden, and fill what we know:
Walkway+%2B+180+=+16%2A24
Walkway=16%2A24-180
highlight_green%28Walkway=204%29 square yards

Use symbols to express the area of the walkway around the garden. Let w = the width of the walkway. Draw a figure if doing so helps you.


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****This is the part we really need to do****:
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%2816-2w%29%2824-2w%29=AreaOfGarden
highlight_green%28%2816-2w%29%2824-2w%29=180%29 really all you need if you just want width of the path around the garden.
4%288-w%29%2812-w%29=180
%288-w%29%2812-w%29=45
96-20w%2Bw%5E2=45
-20w%2Bw%5E2%2B51=0
w%5E2-20w%2B51=0
FACTORABLE!
highlight%28%28w-3%29%28w-17%29=0%29
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The meaningful answer or solution here is highlight%28highlight%28w=3%29%29.