What three numbers have an average of 923?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 923. This means if we add these three numbers together and divide by 3, we should get 923.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 923 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 923 * 3 = x + y + z
- So, the sum of our three numbers should be: 2769
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2769.
Solution 1:
923, 923, 923
Verification:
(923 + 923 + 923) / 3 = 2769 / 3 ≈ 923
This solution is correct!
Solution 2:
923, 923, 923
Verification:
(923 + 923 + 923) / 3 = 2769 / 3 ≈ 923
This solution is correct!
Solution 3:
2215, 223, 331
Verification:
(2215 + 223 + 331) / 3 = 2769 / 3 ≈ 923
This solution is correct!
Solution 4:
2293, 379, 97
Verification:
(2293 + 379 + 97) / 3 = 2769 / 3 ≈ 923
This solution is correct!
Solution 5:
473, 501, 1795
Verification:
(473 + 501 + 1795) / 3 = 2769 / 3 ≈ 923
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 2769 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.