2021 Fall AMC 10B Problem 9

The knights in a certain kingdom come in two colors. \frac{2}{7} of them are red, and the rest are blue. Furthermore, \frac{1}{6} of the knights are magical, and the fraction of red knights who are magical is 2 times the fraction of blue knights who are magical. What fraction of red knights are magical?

\textbf{(A) }\frac{2}{9}\qquad\textbf{(B) }\frac{3}{13}\qquad\textbf{(C) }\frac{7}{27}\qquad\textbf{(D) }\frac{2}{7}\qquad\textbf{(E) }\frac{1}{3}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.