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Homework Help: Area as a function of side w/ relation to cost

  1. Nov 4, 2012 #1
    1. The problem statement, all variables and given/known data
    A security fence is to be built around a rectangular parking lot. The front side of the fence costs $60 per meter and the other three sides cost $30 per meter. The total cost of the fence is budgeted to be $7500.

    Part a).

    Express the area of the lot enclosed by the fence as a function of the length 'x' of the side that cost $60 per meter.


    2. Relevant equations

    A=length*width


    3. The attempt at a solution
    I have scanned and uploaded my attempt/work onto imgur. here


    http://i.imgur.com/SDB9T.jpg


    I have attempted the solution, where I had simplified the equation in relation to the cost I am not entirely sure if after that I had solved for the correct variable ( either y or x), and did I input the equation into the right equation (Area of rectangle as a function of length x).

    Any help would be greatly appreciated. Is my attempt correct?

    *****also, confused when they ask for the area of the lot as a function of the length x. So essentially I only want variable "x" in my area equation?******
     
  2. jcsd
  3. Nov 4, 2012 #2

    Dick

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    You've almost got it. But I don't see why you think l=2x and w=2y? Length is x and width is y.
     
  4. Nov 4, 2012 #3
    What did I do wrong? Can I get a hint? So, I am inputting y=125-1.5x into A= length*w, as w right?
     
  5. Nov 4, 2012 #4

    Dick

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    In what you posted you said A=2x*2y. Not A=xy.
     
  6. Nov 4, 2012 #5
    So, aside form my mistake of A= 2x+2y, replaced with A=xy, my answer should be correct?
     
  7. Nov 4, 2012 #6

    Dick

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    If you work out A=xy, it should be fine.
     
  8. Nov 4, 2012 #7
    Ok, thanks!
     
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