What three numbers have an average of 8?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 8. This means if we add these three numbers together and divide by 3, we should get 8.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 8 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 8 * 3 = x + y + z
- So, the sum of our three numbers should be: 24
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 24.
Solution 1:
8, 8, 8
Verification:
(8 + 8 + 8) / 3 = 24 / 3 ≈ 8
This solution is correct!
Solution 2:
8, 8, 8
Verification:
(8 + 8 + 8) / 3 = 24 / 3 ≈ 8
This solution is correct!
Solution 3:
14, 3, 7
Verification:
(14 + 3 + 7) / 3 = 24 / 3 ≈ 8
This solution is correct!
Solution 4:
15, 4, 5
Verification:
(15 + 4 + 5) / 3 = 24 / 3 ≈ 8
This solution is correct!
Solution 5:
18, 4, 2
Verification:
(18 + 4 + 2) / 3 = 24 / 3 ≈ 8
This solution is correct!
Explanation:
As you can see, there are many possible solutions. We can find more by:
- Choosing any two numbers
- Subtracting their sum from 24 to get the third number
Remember:
- The numbers don't have to be whole numbers.
- They can even be negative (although that might not make sense in some real-world contexts).
- The order of the numbers doesn't matter for the average.