What three numbers have an average of 323?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 323. This means if we add these three numbers together and divide by 3, we should get 323.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 323 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 323 * 3 = x + y + z
- So, the sum of our three numbers should be: 969
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 969.
Solution 1:
323, 323, 323
Verification:
(323 + 323 + 323) / 3 = 969 / 3 ≈ 323
This solution is correct!
Solution 2:
323, 323, 323
Verification:
(323 + 323 + 323) / 3 = 969 / 3 ≈ 323
This solution is correct!
Solution 3:
609, 275, 85
Verification:
(609 + 275 + 85) / 3 = 969 / 3 ≈ 323
This solution is correct!
Solution 4:
196, 250, 523
Verification:
(196 + 250 + 523) / 3 = 969 / 3 ≈ 323
This solution is correct!
Solution 5:
857, 28, 84
Verification:
(857 + 28 + 84) / 3 = 969 / 3 ≈ 323
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 969 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.