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Problem about equation solving

  1. Jul 25, 2017 #1
    1. The problem statement, all variables and given/known data
    What is x ?( Assuming x and y are positive)
    2. Relevant equations
    1000/x=3600 + (3600(y-x)+1000)/x+y


    3. The attempt at a solution

    Calculator gives it as x=5/36 but I cannot find a way to get that?
     
  2. jcsd
  3. Jul 25, 2017 #2

    Ray Vickson

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    Do you mean
    $$ (1): \; \;\; \frac{1000}{x} = 3600 + \frac{3600(y-x) +1000}{x} + y$$
    or do you mean
    $$(2): \; \;\; \frac{1000}{x} = 3600 + \frac{3600(y-x) +1000}{x+ y}$$
    In either case you have only one equation in two unknowns ##x## and ##y##, so there will generally be an infinite number of different solutions. For example, if you put ##y=0## you will get one solution ##x##, if you put ##y = 1000## you will get a different solution ##x##, and so forth. Are you sure you have not left out some important information?
     
  4. Jul 25, 2017 #3

    haruspex

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    In general, yes.
    But here we are given x and y both positive. (1) has no solutions, but (2) has only the given solution for x (y being indeterminate).
    Just multiply it out and simplify. Post your working as far as you get.
     
  5. Jul 26, 2017 #4
    It's the second one. I put it on the calculator and give the result as x=5/36?
    I simplified until x/5=x/36y+ 1/36 but cannot get further
     
    Last edited by a moderator: Jul 26, 2017
  6. Jul 26, 2017 #5

    haruspex

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    I asked you to post your working. It is wrong somewhere.
     
  7. Jul 26, 2017 #6

    cnh1995

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    There is no y in the final equation.
    Post your working so we can see where you went wrong.
     
  8. Jul 26, 2017 #7
    Well starting equation was:
    1000/x=3600+(3600(y-x)+1000)/(x+y)
    Divide all 200
    5/x=18+(18(y-x)+5)/(x+y)
    Can be written as;
    5/x=18+(18y-18x+5)/(x+y)
    Multiply 18 with (x+y)/(x+y)
    5/x=(18x+18y+18y-18x+5)/(x+y)
    5/x=36y+5/(x+y)
     
  9. Jul 26, 2017 #8
    Yes it was wrong as I noticed, I've sent my final work
     
  10. Jul 26, 2017 #9

    haruspex

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    Continue to simplify. Multiply out.
     
  11. Jul 26, 2017 #10
    Okay I've missed the detail. Thanks for all your help
     
  12. Jul 26, 2017 #11
    If we continue
    5x+5y= 36xy + 5x
    Then x=5/36
     
  13. Jul 26, 2017 #12
    Can you explain why do we need information of x and y is positive to derivate that?
     
  14. Jul 26, 2017 #13

    haruspex

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    No, my post#3 was a bit misleading there. That comment only appiled to the other interpretation of the equation given, i.e. (1) in Ray's post.
     
  15. Jul 26, 2017 #14
    Okay. Thanks to everyone who helped.
     
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