A number of 2 digit is increased by 9 when the digits are reversed, the sum of the digit is 5. Find the number
in the original, let the unit digit be x, and the tens digit by y
x + y = 5 , (we can figure it out from here)
original number: 10y+x
number reversed: 10x+y
10x+y - (10y+x) = 9
9x - 9y = 9, or
x - y = 1
add this to x+y=5
2x = 6
x = 3, then y = 2
the original number was 23
(check: reversed would be 32, which is 9 more than the original)