What three numbers have an average of 3?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 3. This means if we add these three numbers together and divide by 3, we should get 3.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 3 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 3 * 3 = x + y + z
- So, the sum of our three numbers should be: 9
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 9.
Solution 1:
3, 3, 3
Verification:
(3 + 3 + 3) / 3 = 9 / 3 ≈ 3
This solution is correct!
Solution 2:
3, 3, 3
Verification:
(3 + 3 + 3) / 3 = 9 / 3 ≈ 3
This solution is correct!
Solution 3:
6, 1, 2
Verification:
(6 + 1 + 2) / 3 = 9 / 3 ≈ 3
This solution is correct!
Solution 4:
1, 7, 1
Verification:
(1 + 7 + 1) / 3 = 9 / 3 ≈ 3
This solution is correct!
Solution 5:
6, 2, 1
Verification:
(6 + 2 + 1) / 3 = 9 / 3 ≈ 3
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 9 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.