What three numbers have an average of 827?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 827. This means if we add these three numbers together and divide by 3, we should get 827.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 827 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 827 * 3 = x + y + z
- So, the sum of our three numbers should be: 2481
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2481.
Solution 1:
827, 827, 827
Verification:
(827 + 827 + 827) / 3 = 2481 / 3 ≈ 827
This solution is correct!
Solution 2:
827, 827, 827
Verification:
(827 + 827 + 827) / 3 = 2481 / 3 ≈ 827
This solution is correct!
Solution 3:
1252, 193, 1036
Verification:
(1252 + 193 + 1036) / 3 = 2481 / 3 ≈ 827
This solution is correct!
Solution 4:
2106, 356, 19
Verification:
(2106 + 356 + 19) / 3 = 2481 / 3 ≈ 827
This solution is correct!
Solution 5:
1184, 648, 649
Verification:
(1184 + 648 + 649) / 3 = 2481 / 3 ≈ 827
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 2481 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.