A fraction becomes 9/11 if 2 is added to both numerator and denominator. If 3 is added to both, it becomes 5/6. Find the original numerator.

Question

Accepted Answer

7. x+2/y+2=9/11 -> 11x - 9y = -4. x+3/y+3=5/6 -> 6x - 5y = -3. Solve: x = 7, y = 9. Check 9/11=9/11 yes; 10/12=5/6 yes.

A fraction becomes $\frac{9}{11}$ if 2 is added to both numerator and denominator. If 3 is added to both, it becomes $\frac{5}{6}$ . Find the original numerator.