Question 836646
Area of the walkway plus area of the garden equals total area of walkway and garden.


{{{Walkway + Garden = CombinedWalkwayAndGarden}}}, and fill what we know:
{{{Walkway + 180 = 16*24}}}
{{{Walkway=16*24-180}}}
{{{highlight_green(Walkway=204)}}} 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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{{{(16-2w)(24-2w)=AreaOfGarden}}}
{{{highlight_green((16-2w)(24-2w)=180)}}} really all you need if you just want width of the path around the garden.
{{{4(8-w)(12-w)=180}}}
{{{(8-w)(12-w)=45}}}
{{{96-20w+w^2=45}}}
{{{-20w+w^2+51=0}}}
{{{w^2-20w+51=0}}}
FACTORABLE!
{{{highlight((w-3)(w-17)=0)}}}
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The meaningful answer or solution here is {{{highlight(highlight(w=3))}}}.