Let's use the variable R to represent the number of rulers, the variable P for the number of protractors and the variable C for the number of calculators.
If the teacher will buy twice as many rulers as protractors, we have the equation:

Then, if the number of calculators is one quarter of the number of protractors, we have:

The total number of itens is 65, so:

Using the values of R and C, we have:

So the teacher bought 20 protractors, 40 rulers and 5 calculators.