There are three main types of algebra average word problems commonly encountered in school or in tests like the SAT: 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 gives an introduction to averages and solves some algebra problems involving averages.

The following videos give examplse of how to solve algebra average problem.

If the average (arithmetic mean) of 8,11,25,and p is 15, find 8+11+25+p and then find p.

If a = 3b = 6c, what is the average (arithmetic mean) of a, b and c in terms of a?

Another type of average problem involves the weighted average - which is the average of two or more terms that do not all have the same number of members. To find the weighted term, multiply each term by its weighting factor, which is the number of times each term occurs.

The formula for weighted average is:

**Example:**

A class of 25 students took a science test. 10 students had an average (arithmetic mean) score of 80. The other students had an average score of 60. What is the average score of the whole class?

**Solution:**

**Step 1:** To get the sum of weighted terms, multiply each average by the number of students that had that average and then sum them up.

80 × 10 + 60 × 15 = 800 + 900 = 1700

**Step 2:** Total number of terms = Total number of students = 25

**Step 3:** Using the formula

**Answer**: The average score of the whole class is 68.

Be careful! You will get the wrong answer if you add the two average scores and divide the answer by two.

This video tutorial shows how to calculate a weighted mean (weighted average)

Fiften accounting majors have an average grade of 90.
Seven marketing majors averaged 85, and ten finance majors averaged 93. What is the weighted mean for the 32 students?

The following shows how to use weighted average to calculate the average score of a student.

Computation of average speed is a trickier type of average problems. Average speed uses the formula:

* Example*:

John drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour. What was his average speed for the whole journey?

**Solution:**

**Step 1:** The formula for distance is

Distance = Rate×Time

Total distance = 50 × 3 + 60 × 2 = 270

**Step 2:** Total time = 3 + 2 = 5

**Step 3:** Using the formula

Answer: The average speed is 54 miles per hour.

Be careful! You will get the wrong answer if you add the two speeds and divide the answer by two.

How to calculate average speed.

The Hubble Space Telescope was launched. 21 years later and it needs repairing. A rocket was sent out it made good progress traveling at a average of 3000 mph . On the way back it was traveling at 1000 mph what was the average speed..?

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