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:
2118, 296, 73
Verification:
(2118 + 296 + 73) / 3 = 2487 / 3 ≈ 829
This solution is correct!
Solution 4:
30, 2060, 397
Verification:
(30 + 2060 + 397) / 3 = 2487 / 3 ≈ 829
This solution is correct!
Solution 5:
1616, 354, 517
Verification:
(1616 + 354 + 517) / 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.