Question 269364
A number consist of two digit whose sum is 5. When the digits are reversed, tne number becomes greater by 9.Find the number:
--------------
It has to be 14 or 23
It's 23
--------------
The difference when you reverse digits is always a multiple of 9.
1*9
2*9
3*9
4*9 etc
The multiplier of 9 is the difference between the digits.
eg, for 37, the difference is 4, so 4*9 will be the change when the digits are reversed.
-------------
For your problem, the multiplier of 9 is 1, so the difference between the digits is 1.
That makes the problem simpler:
---------------------------------
The sum of the digits is 5
The difference of the digits is 1
u + t = 5
u - t = 1
------------ Add
2u = 6
u = 3
t = 2
--> 23
-------------------
The long way:
10t + u = 10u + t - 9
t + u = 5
----------
9t - 9u = -9
t - u = -1
t + u = 5
2t = 4
t = 2
u = 3
--> 23