 # Average Word Problems

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

### Average (Arithmetic Mean)

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.

Examples of average word problems
Examples:
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? How to solve word problems that involve finding the average of a group of numbers?
Examples:
1. All of the members of the Harvey family are very tall. Their heights are 81 inches, 78 inches, 71 inches, 75 inches and 70 inches. What is the average height of the 5 Harveys?

2. There are 5 trees in Terry's front yard. He measures each tree to find out how tall it is in inches and writes the measurement on a sheet of paper. This is Terry's list: 98, 94, 41, 96, and 11. What is the average height of a tree in Terry's front yard?
Word Problems with Averages
Examples:
1. 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?

2. Tracy mowed lawns for 2 hours and earned \$7.40 per hour. Then, she was windows for 3 hours and earned \$6.50 per hour. What were Tracy's average earnings per hour for all 5 hours?

3. After taking 3 quizzes, your average is 72 out of 100. What must your average be on the next five quizzes to increase your average to 77?

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