What three numbers have an average of 849?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 849. This means if we add these three numbers together and divide by 3, we should get 849.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 849 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 849 * 3 = x + y + z
- So, the sum of our three numbers should be: 2547
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2547.
Solution 1:
849, 849, 849
Verification:
(849 + 849 + 849) / 3 = 2547 / 3 ≈ 849
This solution is correct!
Solution 2:
849, 849, 849
Verification:
(849 + 849 + 849) / 3 = 2547 / 3 ≈ 849
This solution is correct!
Solution 3:
2313, 37, 197
Verification:
(2313 + 37 + 197) / 3 = 2547 / 3 ≈ 849
This solution is correct!
Solution 4:
14, 751, 1782
Verification:
(14 + 751 + 1782) / 3 = 2547 / 3 ≈ 849
This solution is correct!
Solution 5:
1271, 1226, 50
Verification:
(1271 + 1226 + 50) / 3 = 2547 / 3 ≈ 849
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 2547 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.