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