What three numbers have an average of 947?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 947. This means if we add these three numbers together and divide by 3, we should get 947.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 947 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 947 * 3 = x + y + z
- So, the sum of our three numbers should be: 2841
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2841.
Solution 1:
947, 947, 947
Verification:
(947 + 947 + 947) / 3 = 2841 / 3 ≈ 947
This solution is correct!
Solution 2:
947, 947, 947
Verification:
(947 + 947 + 947) / 3 = 2841 / 3 ≈ 947
This solution is correct!
Solution 3:
1437, 1159, 245
Verification:
(1437 + 1159 + 245) / 3 = 2841 / 3 ≈ 947
This solution is correct!
Solution 4:
1918, 848, 75
Verification:
(1918 + 848 + 75) / 3 = 2841 / 3 ≈ 947
This solution is correct!
Solution 5:
2736, 31, 74
Verification:
(2736 + 31 + 74) / 3 = 2841 / 3 ≈ 947
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 2841 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.