What three numbers have an average of 992?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 992. This means if we add these three numbers together and divide by 3, we should get 992.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 992 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 992 * 3 = x + y + z
- So, the sum of our three numbers should be: 2976
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2976.
Solution 1:
992, 992, 992
Verification:
(992 + 992 + 992) / 3 = 2976 / 3 ≈ 992
This solution is correct!
Solution 2:
992, 992, 992
Verification:
(992 + 992 + 992) / 3 = 2976 / 3 ≈ 992
This solution is correct!
Solution 3:
2551, 211, 214
Verification:
(2551 + 211 + 214) / 3 = 2976 / 3 ≈ 992
This solution is correct!
Solution 4:
2425, 145, 406
Verification:
(2425 + 145 + 406) / 3 = 2976 / 3 ≈ 992
This solution is correct!
Solution 5:
1730, 893, 353
Verification:
(1730 + 893 + 353) / 3 = 2976 / 3 ≈ 992
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 2976 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.