What three numbers have an average of 839?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 839. This means if we add these three numbers together and divide by 3, we should get 839.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 839 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 839 * 3 = x + y + z
- So, the sum of our three numbers should be: 2517
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2517.
Solution 1:
839, 839, 839
Verification:
(839 + 839 + 839) / 3 = 2517 / 3 ≈ 839
This solution is correct!
Solution 2:
839, 839, 839
Verification:
(839 + 839 + 839) / 3 = 2517 / 3 ≈ 839
This solution is correct!
Solution 3:
559, 538, 1420
Verification:
(559 + 538 + 1420) / 3 = 2517 / 3 ≈ 839
This solution is correct!
Solution 4:
1525, 710, 282
Verification:
(1525 + 710 + 282) / 3 = 2517 / 3 ≈ 839
This solution is correct!
Solution 5:
1093, 1267, 157
Verification:
(1093 + 1267 + 157) / 3 = 2517 / 3 ≈ 839
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 2517 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.