SOLUTION: Hi tony hamid and helen had 48 dollars altogether. Tony had 10 dollars more than hamid and 14 dollars more than helen. When tony gave 2 dollar s to hamid and 6 dollars to helen,

Tony + Hamid  + Helen  = 48


T    + (T-10) + (T-14) = 48


3T - 24 = 48  ====>  3T = 48 + 24 = 72  ====>  T =  = 24.


====>  Tony has 24 dollars.

       Hamid  has  24 - 10 = 14 dollars.

       Helen  has  24 - 14 = 10 dollars.



The problem is just solved.


The last condition  ". . . When Tony gave . . . "  is UNNECESSARY and EXCESSIVE.

It is NOT USED in getting the solution. 


The only thing you should check is whether this unnecessary condition contradicts the obtained solution.


Easy check (DO IT on your own !) shows that it does not contradict. 

In opposite, this part of the solution is CONSISTENT with the obtained solution (fortunately !)


So, the obtained solution is valid !