What three numbers have an average of 647?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 647. This means if we add these three numbers together and divide by 3, we should get 647.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 647 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 647 * 3 = x + y + z
- So, the sum of our three numbers should be: 1941
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1941.
Solution 1:
647, 647, 647
Verification:
(647 + 647 + 647) / 3 = 1941 / 3 ≈ 647
This solution is correct!
Solution 2:
647, 647, 647
Verification:
(647 + 647 + 647) / 3 = 1941 / 3 ≈ 647
This solution is correct!
Solution 3:
1795, 109, 37
Verification:
(1795 + 109 + 37) / 3 = 1941 / 3 ≈ 647
This solution is correct!
Solution 4:
900, 330, 711
Verification:
(900 + 330 + 711) / 3 = 1941 / 3 ≈ 647
This solution is correct!
Solution 5:
430, 300, 1211
Verification:
(430 + 300 + 1211) / 3 = 1941 / 3 ≈ 647
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 1941 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.