What three numbers have an average of 922?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 922. This means if we add these three numbers together and divide by 3, we should get 922.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 922 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 922 * 3 = x + y + z
- So, the sum of our three numbers should be: 2766
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2766.
Solution 1:
922, 922, 922
Verification:
(922 + 922 + 922) / 3 = 2766 / 3 ≈ 922
This solution is correct!
Solution 2:
922, 922, 922
Verification:
(922 + 922 + 922) / 3 = 2766 / 3 ≈ 922
This solution is correct!
Solution 3:
312, 124, 2330
Verification:
(312 + 124 + 2330) / 3 = 2766 / 3 ≈ 922
This solution is correct!
Solution 4:
363, 2003, 400
Verification:
(363 + 2003 + 400) / 3 = 2766 / 3 ≈ 922
This solution is correct!
Solution 5:
840, 1565, 361
Verification:
(840 + 1565 + 361) / 3 = 2766 / 3 ≈ 922
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 2766 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.