2006 AMC 8 Problem 12

Antonette gets 70 \% on a 10-problem test, 80 \% on a 20-problem test and 90 \% on a 30-problem test. If the three tests are combined into one 60-problem test, which percent is closest to her overall score?

\textbf{(A)}\ 40\qquad\textbf{(B)}\ 77\qquad\textbf{(C)}\ 80\qquad\textbf{(D)}\ 83\qquad\textbf{(E)}\ 87

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