High School Math contest division question

[timelesstrix0]

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) + 12the final answers that the teacher told me were that x = 43 and y = 12
can anyone explain how i can solve this please?

 

[mfb]

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).

 

[Deepak suwalka]

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.

 

[DrClaude]

If you have tree 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.

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