What three numbers have an average of 855?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 855. This means if we add these three numbers together and divide by 3, we should get 855.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 855 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 855 * 3 = x + y + z
- So, the sum of our three numbers should be: 2565
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2565.
Solution 1:
855, 855, 855
Verification:
(855 + 855 + 855) / 3 = 2565 / 3 ≈ 855
This solution is correct!
Solution 2:
855, 855, 855
Verification:
(855 + 855 + 855) / 3 = 2565 / 3 ≈ 855
This solution is correct!
Solution 3:
712, 459, 1394
Verification:
(712 + 459 + 1394) / 3 = 2565 / 3 ≈ 855
This solution is correct!
Solution 4:
1135, 1073, 357
Verification:
(1135 + 1073 + 357) / 3 = 2565 / 3 ≈ 855
This solution is correct!
Solution 5:
295, 1006, 1264
Verification:
(295 + 1006 + 1264) / 3 = 2565 / 3 ≈ 855
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 2565 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.