What three numbers have an average of 644?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 644. This means if we add these three numbers together and divide by 3, we should get 644.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 644 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 644 * 3 = x + y + z
- So, the sum of our three numbers should be: 1932
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1932.
Solution 1:
644, 644, 644
Verification:
(644 + 644 + 644) / 3 = 1932 / 3 ≈ 644
This solution is correct!
Solution 2:
644, 644, 644
Verification:
(644 + 644 + 644) / 3 = 1932 / 3 ≈ 644
This solution is correct!
Solution 3:
226, 757, 949
Verification:
(226 + 757 + 949) / 3 = 1932 / 3 ≈ 644
This solution is correct!
Solution 4:
1528, 327, 77
Verification:
(1528 + 327 + 77) / 3 = 1932 / 3 ≈ 644
This solution is correct!
Solution 5:
1279, 236, 417
Verification:
(1279 + 236 + 417) / 3 = 1932 / 3 ≈ 644
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 1932 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.