What three numbers have an average of 123?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 123. This means if we add these three numbers together and divide by 3, we should get 123.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 123 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 123 * 3 = x + y + z
- So, the sum of our three numbers should be: 369
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 369.
Solution 1:
123, 123, 123
Verification:
(123 + 123 + 123) / 3 = 369 / 3 ≈ 123
This solution is correct!
Solution 2:
123, 123, 123
Verification:
(123 + 123 + 123) / 3 = 369 / 3 ≈ 123
This solution is correct!
Solution 3:
311, 16, 42
Verification:
(311 + 16 + 42) / 3 = 369 / 3 ≈ 123
This solution is correct!
Solution 4:
189, 97, 83
Verification:
(189 + 97 + 83) / 3 = 369 / 3 ≈ 123
This solution is correct!
Solution 5:
256, 23, 90
Verification:
(256 + 23 + 90) / 3 = 369 / 3 ≈ 123
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 369 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.