What three numbers have an average of 866?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 866. This means if we add these three numbers together and divide by 3, we should get 866.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 866 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 866 * 3 = x + y + z
- So, the sum of our three numbers should be: 2598
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2598.
Solution 1:
866, 866, 866
Verification:
(866 + 866 + 866) / 3 = 2598 / 3 ≈ 866
This solution is correct!
Solution 2:
866, 866, 866
Verification:
(866 + 866 + 866) / 3 = 2598 / 3 ≈ 866
This solution is correct!
Solution 3:
1024, 808, 766
Verification:
(1024 + 808 + 766) / 3 = 2598 / 3 ≈ 866
This solution is correct!
Solution 4:
2540, 53, 5
Verification:
(2540 + 53 + 5) / 3 = 2598 / 3 ≈ 866
This solution is correct!
Solution 5:
2330, 68, 200
Verification:
(2330 + 68 + 200) / 3 = 2598 / 3 ≈ 866
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 2598 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.