Question: There are $14$ more cookies than biscuits in a jar of $38$ cookies and biscuits. How many cookies are in the jar?

Answer: 
Solve the following system. $$x-y=14$$ and $$x+y=38$$
Think of starting with a jar of $38$ cookies and no biscuits, and turning cookies into biscuits one by one. Each time you do this you reduce the excess of cookies over biscuits by $2$. How many times would you have to do it to make that excess be $14$?