What three numbers have an average of 6?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 6. This means if we add these three numbers together and divide by 3, we should get 6.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 6 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 6 * 3 = x + y + z
- So, the sum of our three numbers should be: 18
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 18.
Solution 1:
6, 6, 6
Verification:
(6 + 6 + 6) / 3 = 18 / 3 ≈ 6
This solution is correct!
Solution 2:
6, 6, 6
Verification:
(6 + 6 + 6) / 3 = 18 / 3 ≈ 6
This solution is correct!
Solution 3:
12, 1, 5
Verification:
(12 + 1 + 5) / 3 = 18 / 3 ≈ 6
This solution is correct!
Solution 4:
1, 10, 7
Verification:
(1 + 10 + 7) / 3 = 18 / 3 ≈ 6
This solution is correct!
Solution 5:
16, 1, 1
Verification:
(16 + 1 + 1) / 3 = 18 / 3 ≈ 6
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 18 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.