Final answer:
Julio started with the number 20. Cubing a number and then taking the cube root of the result returns the original number.
Step-by-step explanation:
If Julio ends with 20 after cubing a number and then taking the cube root of the result, it means that the original number he started with must be 20. This is because the operations of cubing a number and then taking the cube root are inverse operations. Performing these operations one after the other will return the original value. So, the cube root of a number cubed is the number itself.
For example, if Julio starts with the number x, cubes it to get x3, and then takes the cube root of x3, he will end up with the original number x. In this case, since he ends up with 20, this means x equals 20.