What three numbers have an average of 829?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 829. This means if we add these three numbers together and divide by 3, we should get 829.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 829 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 829 * 3 = x + y + z
- So, the sum of our three numbers should be: 2487
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2487.
Solution 1:
829, 829, 829
Verification:
(829 + 829 + 829) / 3 = 2487 / 3 ≈ 829
This solution is correct!
Solution 2:
829, 829, 829
Verification:
(829 + 829 + 829) / 3 = 2487 / 3 ≈ 829
This solution is correct!
Solution 3:
126, 1848, 513
Verification:
(126 + 1848 + 513) / 3 = 2487 / 3 ≈ 829
This solution is correct!
Solution 4:
2168, 98, 221
Verification:
(2168 + 98 + 221) / 3 = 2487 / 3 ≈ 829
This solution is correct!
Solution 5:
1127, 1114, 246
Verification:
(1127 + 1114 + 246) / 3 = 2487 / 3 ≈ 829
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 2487 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.