What three numbers have an average of 854?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 854. This means if we add these three numbers together and divide by 3, we should get 854.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 854 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 854 * 3 = x + y + z
- So, the sum of our three numbers should be: 2562
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2562.
Solution 1:
854, 854, 854
Verification:
(854 + 854 + 854) / 3 = 2562 / 3 ≈ 854
This solution is correct!
Solution 2:
854, 854, 854
Verification:
(854 + 854 + 854) / 3 = 2562 / 3 ≈ 854
This solution is correct!
Solution 3:
2465, 85, 12
Verification:
(2465 + 85 + 12) / 3 = 2562 / 3 ≈ 854
This solution is correct!
Solution 4:
1879, 174, 509
Verification:
(1879 + 174 + 509) / 3 = 2562 / 3 ≈ 854
This solution is correct!
Solution 5:
1512, 722, 328
Verification:
(1512 + 722 + 328) / 3 = 2562 / 3 ≈ 854
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 2562 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.