The POTW Input/Output Machine takes a number as input and adds \(10\) to the number. The machine then takes this sum and multiplies it by \(2\). Finally, the machine takes this product, subtracts \(30\) from the number, and outputs this new number.
Anala and Mei each input a positive integer into the machine. If the sum of their two outputs is \(130\), how many possibilities are there for the positive integer that Anala input into the machine?
Theme: Number Sense