Paul got a box of 457 erasers and 617 crayons for his birthday. At the end of the school year he only had 523 crayons left while not having lost a single eraser. How many more crayons than erasers did he have left?
Let's say that Paul had $x$ crayons at the beginning of the school year. Then he got $457$ erasers and $617$ crayons for his birthday, so at the beginning of the school year he had $x + 617$ crayons in total. 

At the end of the school year he only had $523$ crayons left while not having lost a single eraser. So at the end of the school year he had $523$ crayons and $457$ erasers in total. 

We can write this information as a system of equations: 

$x + 617 = 523 + 457$

$x = 974$

So Paul had $974$ crayons at the beginning of the school year. 

Now we can calculate how many more crayons than erasers he had left. He had $523$ crayons and $457$ erasers left, so he had $523 - 457 = 66$ more crayons than erasers left.