The sum of the digits of a two-digit number is $11$, and when the digits are reversed the difference between the new number and the original is $27$.

1. If you use $t$ to represent the tens digit, and $u$ to represent the units digit, how can you represent one of the numbers?

   Answer (a):

   $10t + u$

2. How can you represent the number with its digits reversed, still using $t$ and $u$?

   Hint (b):

   See part (a). What effect does reversing the digits have?

3. Use the information from the problem and parts (a) and (b) to write two equations that can be used to solve this problem.

   Hint (c):

   How do you write an equation to find the sum of the digits?
   How do you write an equation to find the difference of the numbers?

4. What are the two numbers?

   Answer (d):

   $74$ and $47$