What three numbers have an average of 831?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 831. This means if we add these three numbers together and divide by 3, we should get 831.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 831 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 831 * 3 = x + y + z
- So, the sum of our three numbers should be: 2493
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2493.
Solution 1:
831, 831, 831
Verification:
(831 + 831 + 831) / 3 = 2493 / 3 ≈ 831
This solution is correct!
Solution 2:
831, 831, 831
Verification:
(831 + 831 + 831) / 3 = 2493 / 3 ≈ 831
This solution is correct!
Solution 3:
1497, 302, 694
Verification:
(1497 + 302 + 694) / 3 = 2493 / 3 ≈ 831
This solution is correct!
Solution 4:
583, 1046, 864
Verification:
(583 + 1046 + 864) / 3 = 2493 / 3 ≈ 831
This solution is correct!
Solution 5:
91, 964, 1438
Verification:
(91 + 964 + 1438) / 3 = 2493 / 3 ≈ 831
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 2493 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.