Guess and Check

In some problems, the best way to find the answer is to first make an educated guess.  Next, check to see if your answer works.  If your guess is incorrect, you can then make a more educated guess with the knowledge you have gained from the answers you already checked.

Example:  Xian and Cathy sold 14 tickets altogether to the Alcott chorus concert.  Cathy sold 2 more tickets than Xian. How many tickets did each girl sell?