What three numbers have an average of 819?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 819. This means if we add these three numbers together and divide by 3, we should get 819.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 819 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 819 * 3 = x + y + z
- So, the sum of our three numbers should be: 2457
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2457.
Solution 1:
819, 819, 819
Verification:
(819 + 819 + 819) / 3 = 2457 / 3 ≈ 819
This solution is correct!
Solution 2:
819, 819, 819
Verification:
(819 + 819 + 819) / 3 = 2457 / 3 ≈ 819
This solution is correct!
Solution 3:
1083, 41, 1333
Verification:
(1083 + 41 + 1333) / 3 = 2457 / 3 ≈ 819
This solution is correct!
Solution 4:
1749, 670, 38
Verification:
(1749 + 670 + 38) / 3 = 2457 / 3 ≈ 819
This solution is correct!
Solution 5:
59, 1295, 1103
Verification:
(59 + 1295 + 1103) / 3 = 2457 / 3 ≈ 819
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 2457 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.