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Lesson Example Discussion Quiz: Class Homework

Example

Title: Averages

Grade: 8-a Lesson: S3-L1

Explanation: Here are some examples of the topic with images and steps in sequence.

Examples:

Example: 1a

Timothy’s average score on the first four tests was 76. On the next 5 tests, his average score was 85. What was his average score on all the 9 tests?

Average score of 4 tests = 76
Total score of 4 tests = \$76 \times 4 = 304\$
Average score of 5 tests = 85
Total score of 5 tests =\$85 \times 5 = 425\$
Total number of tests = 5 + 4 = 9
Total score of 9 tests = \$304 + 425 = 729\$
Average score of 9 tests = \$729/9 = 81\$

Explanation: In the above problem, Timothy’s average score on the first four tests was 76, and for the next 5 tests, his average score was 85. The total score of 9 tests is 729, and the average score of the total 9 tests is 81.

Example: 2a

After taking 7 quizzes, your average is 75 out of 100. What must your average score be on the next five quizzes to increase your average to 80?

Average score for first 7 Quizzes = 75
Total score of your first 7 quizzes = \$75 \times 7 = 525\$
Total number of quizzes = 7+5 = 12
Total score for 12 quizzes = \$12 \times 80 = 960\$
Score needed in the last 5 quizzes = 960 - 525 = 435
Average score = \$435 \div 5 = 87\$

Explanation: In the above problem, the average score for 7 quizzes is 75 out of 100, and the next average score for 5 quizzes increases to 80. The total average score for 5 quizzes is 87.

Example: 3a

The average of six numbers is 100, and the average of four of these numbers is 80. What is the average of the other two numbers?

Average of 6 numbers = 100
Total sum of six numbers = \$6 \times 100 = 600\$
Average score of these 4 numbers = 80
Total sum of four numbers = \$4 \times 80 = 320\$
Sum of the other two numbers = 600 - 320 = 280
Average of the other 2 numbers = \$280 \div 2 = 140\$

Explanation: In the above problem, the average of six numbers is 100, and the average of four of these numbers is 80. Hence, the average of the other two numbers is 140.