Question 568218
Let the number be N and let its digits be x (tens) and y (ones).  Then,
{{{N=10x+y}}}
We can create two equations from what's given,
{{{x+y=11}}}
{{{10y+x=45+N=45+10x+y}}}
So,
{{{x+y=11}}}
{{{9y-9x=45}}}
Multiply the 1st eqn by 9 and add it to the second to get,
{{{x+y=11}}}
{{{18y=144}}}
Divide the second by 9 to get y=8.  Then, we have
{{{x+8=11}}}
So,
{{{x=3}}}
So, the original number was 38.