2021 Gauss 8 Problem 19

Asima and Nile each think of an integer greater than 0. Each of them performs the following operations on their integer: they double it, then subtract 10, and then multiply it by 4. The sum of their results is 440. How many possibilities are there for Asima's original integer?

\textbf{(A)}\ 64\quad \textbf{(B)}\ 44\quad \textbf{(C)}\ 65\quad \textbf{(D)}\ 45\quad \textbf{(E)}\ 66

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.