2016 AMC 8 Problem 12

Jefferson Middle School has the same number of boys and girls. \frac{3}{4} of the girls and \frac{2}{3} of the boys went on a field trip. What fraction of the students on the field trip were girls?

\textbf{(A) }\frac{1}{2}\qquad\textbf{(B) }\frac{9}{17}\qquad\textbf{(C) }\frac{7}{13}\qquad\textbf{(D) }\frac{2}{3}\qquad \textbf{(E) }\frac{14}{15}

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