AoPSWiki
Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams?
Check out Art of Problem Solving's Introduction to Algebra by Richard Rusczyk.

2005 AMC 12B Problems/Problem 4

From AoPSWiki

Problem

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

Solution

Lisa's goal was to get an A on 80\% \cdot 50 = 40 quizzes. She already has A's on 22 quizzes, so she needs to get A's on 40-22=18 more. There are 50-30=20 quizzes left, so she can afford to get less than an A on 20-18=\boxed{2} of them.

See also

Want to learn how to tackle those tough AMC/AIME/Olympiad counting and probability problems? Check out Art of Problem Solving's Intermediate Counting & Probability by David Patrick.
© Copyright 2008 AoPS Incorporated. All Rights Reserved. • FoundationPrivacyContact Us