What three numbers have an average of 843?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 843. This means if we add these three numbers together and divide by 3, we should get 843.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 843 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 843 * 3 = x + y + z
- So, the sum of our three numbers should be: 2529
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2529.
Solution 1:
843, 843, 843
Verification:
(843 + 843 + 843) / 3 = 2529 / 3 ≈ 843
This solution is correct!
Solution 2:
843, 843, 843
Verification:
(843 + 843 + 843) / 3 = 2529 / 3 ≈ 843
This solution is correct!
Solution 3:
769, 1060, 700
Verification:
(769 + 1060 + 700) / 3 = 2529 / 3 ≈ 843
This solution is correct!
Solution 4:
974, 37, 1518
Verification:
(974 + 37 + 1518) / 3 = 2529 / 3 ≈ 843
This solution is correct!
Solution 5:
327, 1016, 1186
Verification:
(327 + 1016 + 1186) / 3 = 2529 / 3 ≈ 843
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 2529 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.