The sum of the digits in a two digit number is 11. if the digits are reversed, the new number will be 45 less than the original number. what is the original number

If the digits are x and y then

x+y=11 or x=11-y (we will use this later)

if x is tens and y is ones digit then the original number can be represented as 10x+y
reversing 10s place and ones place gives 10y+x, and reversing make it 45 less so
10x+y=45+10y+x
if we combine that with the other equation, we get
10(11-y)+y=45+10y+(11-y)
expand
110-9y=56+9y
add 9y to both sides
110=56+18y
minus 56
54=18y
divide by 18
3=y
sub back into x=11-y
x=11-3
x=8

the original number is 83