Paul got a box of w erasers and x crayons for his birthday. At the end of the school year he only had y crayons left while not having lost a single eraser. How many more crayons than erasers did he have left?
Paul got a box of w erasers and x crayons for his birthday.

Let's introduce the number of erasers and crayons that he had at the beginning of the school year:

e_0 - number of erasers at the beginning of the school year,
c_0 - number of crayons at the beginning of the school year.

At the end of the school year he only had y crayons left while not having lost a single eraser. How many more crayons than erasers did he have left?

e_1 - number of erasers at the end of the school year,
c_1 - number of crayons at the end of the school year.

We know that:

e_0 + x = w,
c_0 - y = 0.

From the condition of the problem we can conclude that:

e_1 = e_0,
c_1 = c_0 - y.

We also know that:

e_0 = w - x,
c_0 = x.

Now we can find c_1:

c_1 = x