From the first two sentences


    "The sum of 3 numbers is 30. The sum of the first and second is twice the third."


it is CLEAR that  


    (First + Second + Third) = (First+Second) + Third = 2*Third + Third = 3*Third = 30,


which implies  that Third = 10.


So the "Third" number is found MENTALLY and MOMENTARILY without using equations.


But it is NOT ENOUGH to complete the solution.


The complete solution must assure that the second and the third numbers EXIST and that the problem is not SELF-CONTRADICTORY.


For it, the second and the third numbers should be found.


By knowing the THIRD, it is just problem for 2 equations in 2 unknowns.


The solution DOES EXIST, indeed, and it is  FIRST = 9  and SECOND = 11.



At this point, the solution is, finally, completed.