Hi Elizabeth, if the average for the first 7 quizzes was 88%, that means the total number of points earned for the first 7 quizzes was 616 points. We know this because average is total number of points divided by the number of quizzes.
When we divide the total points for all ten quizzes by 10, we want to get 90%. The question is what is the total number of points needed when divided by 10 gives us 90%?
90 (final average) = (616 + x) / 10, where x represents the number of points needed from the final three quizzes.
Multiply both sides by 10 to clear the fraction.
900 = 616 + x
Subtract 616 from both sides of the equation:
284 = x, where x represents the total score on the last three quizzes. To find the average we need on the final three quizzes, divide 284 by 3, giving 94.
You need to score an average of 94 on each of the final three quizzes to end up with a final average for the semester of 90%.