Question 275504
<br>
While a formal algebraic solution was probably wanted, note that you can also work this problem using logical reasoning and the basic process of adding two 2-digit numbers.  In "coded" form, you have this addition, where A and B are the two digits of the original number and S is the sum of those two digits (S is not a digit, because the sum of the two 2-digit numbers is 3 digits):<br><pre>
   A B
 + B A
 ------
   S S</pre>
Now that sum has the sum "S" in the 10s column and also in the units column, so the value of that sum is 10S + 1S = 11S.<br>
But the sum is 132, so 11S = 132, so S = 132/11 = 12.<br>
So we know that the sum of the two digits A and B is 12.<br>
However, we have no other information to use to find a unique solution to the problem.  So the original number can be any 2-digit number in which the sum of the two digits is 12: 39, 48, 57, 66, 75, 84, or 93.  Notice that the statement of the problem did not require the two digits of the original number to be different, so 66 is one of the possible answers.<br>
ANSWERS: any of the numbers 39, 48, 57, 66, 75, 84, or 93<br>