SOLUTION: The sum of the digits of a certain two digit number is 7. Reversing its digits increases the number by 9. What is the number? I've almost pulled out all my hair on this problem.

Question 509226: The sum of the digits of a certain two digit number is 7. Reversing its digits increases the number by 9. What is the number? I've almost pulled out all my hair on this problem. Thanks for helping me.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The sum of the digits of a certain two digit number is 7. Reversing its digits increases the number by 9. What is the number?
----
Let the number be 10t+u where t is the tens and u is the units digit.
---
Equations:
t + u = 7
(10u+t)-(10t+u) = 9
----
Rearrange:
t + u = 7
-9t+9u = 9
----
Modify:
t + u = 7
t - u = -9
----
2t = -2
t = -1
----
Comment: That cannot be.
----------------------------------
It looks like reversing the digits DECREASED the value rather thaen INcreased
the value.
===============
Cheers,
Stan H.
=====================