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# Simple Word Problem- Double check answer?

Posted 10 years ago
 Hello, I was just wondering if someone can double check my answer on this word problem. Thank you. You have a rectangular garden that is 25ft by 11ft. You want to build a pathway around the garden. However, you only have enough gravel to build 576 ft. So, how wide can your pathway around the garden be? What I did was find the perimeter. P=72 ft So, then I just divided 576 by 72 and I got 8. My answer was that the pathway had to be 8 ft wide. Is that correct?
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Posted 10 years ago
 Alternatively we could do it this way, look at diagram 2 (11 * x) + 2 (25 * x) + 4 x^2 = 576 giving 4 x^2 + 72 x - 576 = 0 We could simplify it to x^2 + 18 x - 144 = 0 Solve either by hand or Solve[x^2 + 18 x - 144 == 0, x] {{x -> -24}, {x -> 6}} and clearly x can't be -24 so there you have the answer.Paul.
Posted 10 years ago
 For a path of width w the total area (path plus enclosed area) is (25+2w)(11+2*w) and the enclosed area is (25)(11). The difference is given as 576. eqn = (25 + 2 w)*(11 + 2 w) - (25*11) == 576; soln = Solve[{eqn, w > 0}, w][[1]]  {w -> 6} eqn /. soln  True So the path is 6 ft wide.