What three numbers have an average of 919?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 919. This means if we add these three numbers together and divide by 3, we should get 919.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 919 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 919 * 3 = x + y + z
- So, the sum of our three numbers should be: 2757
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2757.
Solution 1:
919, 919, 919
Verification:
(919 + 919 + 919) / 3 = 2757 / 3 ≈ 919
This solution is correct!
Solution 2:
919, 919, 919
Verification:
(919 + 919 + 919) / 3 = 2757 / 3 ≈ 919
This solution is correct!
Solution 3:
2512, 195, 50
Verification:
(2512 + 195 + 50) / 3 = 2757 / 3 ≈ 919
This solution is correct!
Solution 4:
283, 2070, 404
Verification:
(283 + 2070 + 404) / 3 = 2757 / 3 ≈ 919
This solution is correct!
Solution 5:
1922, 584, 251
Verification:
(1922 + 584 + 251) / 3 = 2757 / 3 ≈ 919
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 2757 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.