SOLUTION: a 2 digit number is 3 times the sum of its digits. The number is also less 45 less than the number formed by reversing the digits original number. What is the original number?

Let the tens digit be t and the units digit be u.  Then the number
is 10t+u.

10t+u

equals

 3(t+u)

So that says

10t+u = 3(t+u)

10t+u = 3t+3u

   7t = 2u

   

So the only way that can be is t=2 and u=7

Let's see.  If we reverse 27 we get 72 and 72-27 = 45, so yes that is true of 27.

27

Edwin