The 2008 AMC 10 will be scored by awarding 5 points for each correct response, 0 points for each incorrect response, and 2 points for each problem left unanswered. After looking over the 30 problems, Alex has decided to attempt the first 25 and leave only the last 5 unanswered. How many of the first 25 problems must he solve correctly in order to score at least 110 points?