Question 861265
* THIS WHOLE SOLUTION IS NOW CORRECTED!  

The garden itself is 24*40 square feet.


Draw a picture if it helps, best thing to do.
Outside dimensions of the walkway will be 24+2w by 40+2w, using w as the width of the walkway.


Accounting for the areas, the difference in areas will be the area for the available concrete material to form the walkway:


{{{highlight_green((2w+24)(2w+40)-(24)(40)=3975)}}}.
This can be simplified and then solved for w.
{{{4w^2+48w+80w+24*40-24*40=3975}}}
{{{4w^2128w-3975=0}}}
Discriminant is 128^2+4*4*9875=79984.
This discriminant is 4*4*4999.


Using general solution and taking the form with the positive square root,
{{{w=(-128+sqrt(4*4*4999))/(2*4)}}}
{{{w=(-128+4sqrt(4999))/(2*4)}}}
{{{highlight(w=(-32+sqrt(4999))/2)}}} Which as an approximation can be stated as 19.35.

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