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More Lessons for Algebra, Math Worksheets

There are three main types of average problems commonly encountered in school algebra: Average (Arithmetic Mean), Weighted Average and Average Speed.### Average (Arithmetic Mean)

Example:

1) The table below shows the total number of goals scored in each of 43 soccer matches in a regional tournament. What is the average number of goals scored per match, to the nearest 0.1 goal?

2) Tom has taken 5 of the 8 equally weighted test in his U.S. History class this semester, and he has an average score of exactly 78.0 points. How many points does he need to earn on the 6th test to bring his average score to exactly 80.0 points?

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Algebra, Math Worksheets

There are three main types of average problems commonly encountered in school algebra: Average (Arithmetic Mean), Weighted Average and Average Speed.

The average (arithmetic mean) uses the formula:

The formula can also be written as

Example :

The average (arithmetic mean) of a list of 6 numbers is 20. If we remove one of the numbers, the average of the remaining numbers is 15. What is the number that was removed?

Solution:

Step 1: The removed number could be obtained by difference between the sum of original 6 numbers and the sum of remaining 5 numbers i.e.

sum of original 6 numbers – sum of remaining 5 numbers

Step 2: Using the formula

sum of original 6 numbers =20 × 6 = 120

sum of remaining 5 numbers= 15 × 5 = 75

Step 3: Using the formula from step 1

*Number removed = sum of original 6 numbers – sum of remaining 5 numbers *

120 – 75 = 45

Answer: The number removed is 45.

The following video shows more examples of average word problems:Example:

1) The table below shows the total number of goals scored in each of 43 soccer matches in a regional tournament. What is the average number of goals scored per match, to the nearest 0.1 goal?

2) Tom has taken 5 of the 8 equally weighted test in his U.S. History class this semester, and he has an average score of exactly 78.0 points. How many points does he need to earn on the 6th test to bring his average score to exactly 80.0 points?

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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