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