SOLUTION: a concrete walk of uniform width around a rectangular garden that measures 24 by 40 feet is to be built. You have available concrete mix of 3975 square foot. How wide should the co

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Question 861265: a concrete walk of uniform width around a rectangular garden that measures 24 by 40 feet is to be built. You have available concrete mix of 3975 square foot. How wide should the concrete walk be to use up all the concrete mix?
Answer by josgarithmetic(39616) About Me  (Show Source):
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* 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%28%282w%2B24%29%282w%2B40%29-%2824%29%2840%29=3975%29.
This can be simplified and then solved for w.
4w%5E2%2B48w%2B80w%2B24%2A40-24%2A40=3975
4w%5E2128w-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=%28-128%2Bsqrt%284%2A4%2A4999%29%29%2F%282%2A4%29
w=%28-128%2B4sqrt%284999%29%29%2F%282%2A4%29
highlight%28w=%28-32%2Bsqrt%284999%29%29%2F2%29 Which as an approximation can be stated as 19.35.
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