What three numbers have an average of 997?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 997. This means if we add these three numbers together and divide by 3, we should get 997.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 997 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 997 * 3 = x + y + z
- So, the sum of our three numbers should be: 2991
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2991.
Solution 1:
997, 997, 997
Verification:
(997 + 997 + 997) / 3 = 2991 / 3 ≈ 997
This solution is correct!
Solution 2:
997, 997, 997
Verification:
(997 + 997 + 997) / 3 = 2991 / 3 ≈ 997
This solution is correct!
Solution 3:
2636, 275, 80
Verification:
(2636 + 275 + 80) / 3 = 2991 / 3 ≈ 997
This solution is correct!
Solution 4:
300, 1012, 1679
Verification:
(300 + 1012 + 1679) / 3 = 2991 / 3 ≈ 997
This solution is correct!
Solution 5:
2985, 1, 5
Verification:
(2985 + 1 + 5) / 3 = 2991 / 3 ≈ 997
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 2991 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.