Mom and Daughter

We will let Terry's age be $10a+b$ and Sherry's age be $10b+a$ so that Terry's age in reverse will be Sherry's age ( $a$ represents the tens digit of Terry's age and $b$ represents its ones digit). In 13 years, Terry will be $10a+b+13$ and Sherry will be $10b+a+13$ . Based on the condition that at this point in time Terry is half as old as Sherry, we get the equation $2(10a+b+13) = 10b+a+13$ which simplifies to $19a+13 = 8b$ . Since $a$ and $b$ can each only be a single digit number, we cat easily apply guess and check to find that $a=1$ and $b=4$ . Therefore, Terry is currently $\boxed{14}$ years old.

All single digits in reverse are themselves x10, which is not what we want. Ex: 09 -> 90 Let's take all the values of the first double digits up to 19 (excluding multiples of 10) and find their reverse digits.

Now let's add 13 to the numbers and their reverses.

The only original value for Terry that was half of Sherry's age after adding 13 is 14.