problem: The sum of two numbers is 25 and their difference is 11. What is the smaller of the two numbers?
solution: Let $x,y$ be the two numbers, $x>y$. Then $x+y=25$ and $x-y=11$, thus:
  
  $y=\frac{1}{2}\left((x+y)-(x-y)\right)=\frac{1}{2}(25-11)=\boxed{7}$.