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B Math contest division question

  1. Sep 28, 2016 #1
    The question is : If x > 0 and I divide x by y, the quotient is 3 and remainder is 7. If I divide y by x the remainder is 12. what is the value of x?

    So far I used long division quotient form to make 2 equations....

    1. x/y = 3 + 7/y
    2. y/x = Q(quotient) + 12/x

    so 1st equation i solve for y and get y = x/3 - 7/3
    2nd equation i solve for y and get y = Q(x) + 12

    the final answers that the teacher told me were that x = 43 and y = 12
    can anyone explain how i can solve this please?
  2. jcsd
  3. Sep 28, 2016 #2


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    2016 Award

    Staff: Mentor

    I would multiply the first equation by y and the second equation by x to get rid of fractions. Afterwards you can plug the expression for x from the first equation into the second equation and look for possible values of y (in both equations).
  4. Oct 6, 2016 #3
    If you have three variables then you should also have three equations.
    Here, you have three variables(x, y, and Q) but two equations. Plz make sure the value of Q is given or not.
    Last edited by a moderator: Oct 6, 2016
  5. Oct 6, 2016 #4


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    Staff: Mentor

    There are only two equations, but there is an assumption that x,y,Q ∈ ℕ, which limits the problem to a single solution.
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