Question 127974
Let's say the original number is ab, so a is the tens digit and b is the ones digit.  That means the reversed number is ba, where b is  tens and a is ones.  Look at the number 35.  3 is the tens and 5 is the ones, so the total is 3(10)+5(1)=30+5=35.  So ba must actually be 10b+a.  We know this is 9 more than the original, so 10b+a=10a+b+9.  If the digits add to 11, a+b=11.
Now we have a system of 2 equations: 10b+a=10a+b+9 and a+b=11.  Using the first, 10b+a=10a+b+9 becomes 9b=9a+9, divide by 9 and get b=a+1.  Plug that b into a+b=11 and get a+(a+1)=11, so 2a+1=11, so 2a=10, and finally, a=5.  If a=5, since a+b=11, b=6.  So the original number was 56.  Check if this is right: 65-56=9, and 5+6=11.  Nicely done!:)