Question 68268

Let x = the 1st digit; y = 2nd digit
:
"The sum of the digits of a two-digit counting number was 9."
x + y = 9
x = (9 - y) 
:
original number: 10x + y
Reversed number: 10y + x
:
"the digits were reversed, the new number was 45 less than the original number"
(10y + x) + 45 = 10x + y
:
Perform operations to get variables on the left and number on the right
10y - y + x - 10x = -45
9y - 9x = -45
:
Simplify divide equation by 9:
y - x = -5
:
Substitute (9-y) for x:
y - (9-y) = -5
y - 9 + y = -5
2y = -5 + 9
2y = +4
y = 2
:
Find x: 9 - 2 = 7
:
Original number 72, reversed number 27
:
Check: 72 - 27 = 45