2005 AMC 10B Problem 6

Question

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?

1

2

3

4

5

Find how many A’s she needs in total

She needs

0.8\cdot50

A’s, and

20

quizzes remain

Lisa needs an A on at least

0.8 \cdot 50 = 40

quizzes.

She already has

22,

so she needs

40 - 22 = 18

A’s among the remaining

20

quizzes.

That leaves at most

20 - 18 = 2

quizzes with a grade lower than an A.

Thus, B is the correct answer.

Problem 6 in other years