What three numbers have an average of 907?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 907. This means if we add these three numbers together and divide by 3, we should get 907.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 907 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 907 * 3 = x + y + z
- So, the sum of our three numbers should be: 2721
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2721.
Solution 1:
907, 907, 907
Verification:
(907 + 907 + 907) / 3 = 2721 / 3 ≈ 907
This solution is correct!
Solution 2:
907, 907, 907
Verification:
(907 + 907 + 907) / 3 = 2721 / 3 ≈ 907
This solution is correct!
Solution 3:
1305, 658, 758
Verification:
(1305 + 658 + 758) / 3 = 2721 / 3 ≈ 907
This solution is correct!
Solution 4:
1197, 1324, 200
Verification:
(1197 + 1324 + 200) / 3 = 2721 / 3 ≈ 907
This solution is correct!
Solution 5:
569, 1116, 1036
Verification:
(569 + 1116 + 1036) / 3 = 2721 / 3 ≈ 907
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 2721 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.