2004 Cayley Problem 20

An archery target has 3 regions, each worth a different value if it is hit. Three archers shoot two arrows each and record scores as follows:

First archer: 1 arrow in C and 1 arrow in A for a score of 15 points

Second archer: 1 arrow in C and 1 arrow in B for a score of 18 points

Third archer: 1 arrow in B and 1 arrow in A for a score of 13 points

If a fourth archer shoots 2 arrows into ring B, her score is

\textbf{(A)}\ 10\quad \textbf{(B)}\ 14\quad \textbf{(C)}\ 16\quad \textbf{(D)}\ 18\quad \textbf{(E)}\ 20

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.