The sum of the difits of a three digit number is 9. if the digits are reversed, the number increases by 495. the sum of the tens digit and the hundreds digit is half the units digit. find the number

Call h the hundreds digit, t the tens digit, and o the ones digit. then the number is 100h+10t+o.
the sum of the digits is 9, our h+t+o=9. if we reverse the digits our new number is 100o+10t+h and this number is 495 larger than the first. we are also given that h+t=½o. put it all together to get
100h+10t+o+495=100o+10t+h
99h-99o=-495
h-o=-5
1h+0t-1o=-5
1h+1t+1o=9
1h+1t-.5o=0

now I put this all in an augmented matrix and write it in reduced row echelon form (I'll spare you the gory details, you can use substitution and elimination if you'd rather). I get the original number to be 126

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