AMC 12 2010a Problem 5

Halfway through a 100-shot archery tournament, Chelsea leads by 50 points. For each shot a bullseye scores 10 points, with other possible scores being 8, 4, 2, and 0 points. Chelsea always scores at least 4 points on each shot. If Chelsea's next $n$ shots are bullseyes she will be guaranteed victory. What is the minimum value for $n$?

\textbf{(A)}\ 38 \textbf{(B)}\ 40 \textbf{(C)}\ 42 \textbf{(D)}\ 44 \textbf{(E)}\ 46