2016 AMC 8 Problem 14

Karl's car uses a gallon of gas every 35 miles, and his gas tank holds 14 gallons when it is full. One day, Karl started with a full tank of gas, drove 350 miles, bought 8 gallons of gas, and continued driving to his destination. When he arrived, his gas tank was half full. How many miles did Karl drive that day?

\textbf{(A)}\ 525\qquad\textbf{(B)}\ 560\qquad\textbf{(C)}\ 595\qquad\textbf{(D)}\ 665\qquad\textbf{(E)}\ 735

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