2014 Cayley Problem 13

In a factory, Erika assembles 3 calculators in the same amount of time that Nick assembles 2 calculators. Also, Nick assembles 1 calculator in the same amount of time that Sam assembles 3 calculators. How many calculators in total can be assembled by Nick, Erika and Sam in the same amount of time as Erika assembles 9 calculators?

\textbf{(A)}\ 30\quad \textbf{(B)}\ 24\quad \textbf{(C)}\ 27\quad \textbf{(D)}\ 81\quad \textbf{(E)}\ 33

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 Cayley contests here.