What three numbers have an average of 127?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 127. This means if we add these three numbers together and divide by 3, we should get 127.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 127 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 127 * 3 = x + y + z
- So, the sum of our three numbers should be: 381
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 381.
Solution 1:
127, 127, 127
Verification:
(127 + 127 + 127) / 3 = 381 / 3 ≈ 127
This solution is correct!
Solution 2:
127, 127, 127
Verification:
(127 + 127 + 127) / 3 = 381 / 3 ≈ 127
This solution is correct!
Solution 3:
113, 139, 129
Verification:
(113 + 139 + 129) / 3 = 381 / 3 ≈ 127
This solution is correct!
Solution 4:
28, 74, 279
Verification:
(28 + 74 + 279) / 3 = 381 / 3 ≈ 127
This solution is correct!
Solution 5:
180, 154, 47
Verification:
(180 + 154 + 47) / 3 = 381 / 3 ≈ 127
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 381 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.