What three numbers have an average of 857?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 857. This means if we add these three numbers together and divide by 3, we should get 857.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 857 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 857 * 3 = x + y + z
- So, the sum of our three numbers should be: 2571
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2571.
Solution 1:
857, 857, 857
Verification:
(857 + 857 + 857) / 3 = 2571 / 3 ≈ 857
This solution is correct!
Solution 2:
857, 857, 857
Verification:
(857 + 857 + 857) / 3 = 2571 / 3 ≈ 857
This solution is correct!
Solution 3:
2101, 153, 317
Verification:
(2101 + 153 + 317) / 3 = 2571 / 3 ≈ 857
This solution is correct!
Solution 4:
1451, 695, 425
Verification:
(1451 + 695 + 425) / 3 = 2571 / 3 ≈ 857
This solution is correct!
Solution 5:
2014, 515, 42
Verification:
(2014 + 515 + 42) / 3 = 2571 / 3 ≈ 857
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 2571 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.