What three numbers have an average of 798?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 798. This means if we add these three numbers together and divide by 3, we should get 798.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 798 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 798 * 3 = x + y + z
- So, the sum of our three numbers should be: 2394
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2394.
Solution 1:
798, 798, 798
Verification:
(798 + 798 + 798) / 3 = 2394 / 3 ≈ 798
This solution is correct!
Solution 2:
798, 798, 798
Verification:
(798 + 798 + 798) / 3 = 2394 / 3 ≈ 798
This solution is correct!
Solution 3:
1382, 1004, 8
Verification:
(1382 + 1004 + 8) / 3 = 2394 / 3 ≈ 798
This solution is correct!
Solution 4:
2239, 47, 108
Verification:
(2239 + 47 + 108) / 3 = 2394 / 3 ≈ 798
This solution is correct!
Solution 5:
1655, 55, 684
Verification:
(1655 + 55 + 684) / 3 = 2394 / 3 ≈ 798
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 2394 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.