2005 AMC 10B Problem 6

At the beginning of the school year, Lisa's goal was to earn an A on at least 80\% of her 50 quizzes for the year. She earned an A on 22 of the first 30 quizzes. If she is to achieve her goal, on at most how many of the remaining quizzes can she earn a grade lower than an A?

\mathrm{(A)} 1 \qquad \mathrm{(B)} 2 \qquad \mathrm{(C)} 3 \qquad \mathrm{(D)} 4 \qquad \mathrm{(E)} 5

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