AMC 12 2004a Problem 2

On the AMC 12, each correct answer is worth $6$ points, each incorrect answer is worth $0$ points, and each problem left unanswered is worth $2.5$ points. If Charlyn leaves $8$ of the $25$ problems unanswered, how many of the remaining problems must she answer correctly in order to score at least $100$?

$\text{(A) } 11 \text{(B) } 13 \text{(C) } 14 \text{(D) } 16 \text{(E) } 17$