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:
905, 1508, 80
Verification:
(905 + 1508 + 80) / 3 = 2493 / 3 ≈ 831
This solution is correct!
Solution 4:
713, 518, 1262
Verification:
(713 + 518 + 1262) / 3 = 2493 / 3 ≈ 831
This solution is correct!
Solution 5:
1431, 513, 549
Verification:
(1431 + 513 + 549) / 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.