Question 5
The $2007$ AMC $12$ contests will be scored by awarding $6$ points for each correct response, $0$ points for each incorrect response, and $1.5$ points for each problem left unanswered. After looking over the $25$ problems, Sarah has decided to attempt the first $22$ and leave the last $3$ unanswered. How many of the first $22$ problems must she solve correctly in order to score at least $100$ points?