Math question? Can you explain the steps???

Question

The hundreds digit of a 3-digit number is 2 more than the tens digit which is half of the ones digit. If the digits are reversed the new number is 198 more than the original number. Find the original number.

Answer 1

648 is the original number. I basically did a guess and check method because there aren't that many possibilities.   I started with the first possibly hundreds digit, which would be 3 in order to follow the pattern, so 1 would be the tens digit and 2 would be the ones.  The reason I didn't start with 2 in the hundreds' position is then we would have 0 as the tens position and 0 is not half of any number for the the ones.  I just kept trying combinations such as... 312,424,536, and finally came to 648 before I found a number that met all the requirements.