What three numbers have an average of 911?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 911. This means if we add these three numbers together and divide by 3, we should get 911.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 911 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 911 * 3 = x + y + z
- So, the sum of our three numbers should be: 2733
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2733.
Solution 1:
911, 911, 911
Verification:
(911 + 911 + 911) / 3 = 2733 / 3 ≈ 911
This solution is correct!
Solution 2:
911, 911, 911
Verification:
(911 + 911 + 911) / 3 = 2733 / 3 ≈ 911
This solution is correct!
Solution 3:
648, 1256, 829
Verification:
(648 + 1256 + 829) / 3 = 2733 / 3 ≈ 911
This solution is correct!
Solution 4:
1722, 626, 385
Verification:
(1722 + 626 + 385) / 3 = 2733 / 3 ≈ 911
This solution is correct!
Solution 5:
1206, 475, 1052
Verification:
(1206 + 475 + 1052) / 3 = 2733 / 3 ≈ 911
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 2733 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.