Can you please help me with this question?

Question

Jasmine's algebra teacher gives pop quizzes that are scored between 0 and 50 points, inclusive. After the first 5 quizzes, Jasmine's quiz average (arithmetic mean) is 35. What is the lowest score jasmine can receive on the 6th quiz and still be able to have an average of at least 45 for the next 20 quizzes?

Answer 1

In order for Jasmine to have an average of 45 for all 20 class quizzes, she needs to have a total score of 45 * 20 = 900 points, out of a total 50 * 20 = 1000 points at stake.

An average of 35 on the first five quizzes means that she has earned a total of 35 * 5 = 175 points on those quizzes. These count toward the required 900, so this means that she needs to earn a total of 900 - 175 = 725 points on the next 15 quizzes. (The total points at stake for those 15 quizzes is 15 * 50 = 750.)

To get the lowest score on the sixth quiz and still end up having earned a total of 725 points on the last 15 quizzes (or 900 points on all 20 quizzes), she needs to earn a perfect 50 on all quizzes from the seventh one onward, which is 14 quizzes. Doing so will earn 14 * 50 = 700 points, leaving us 25 points short of the minimum required 725. This means that the lowest possible score that can be earned on the sixth quiz is 725 - 700 = 25 points.