What three numbers have an average of 339?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 339. This means if we add these three numbers together and divide by 3, we should get 339.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 339 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 339 * 3 = x + y + z
- So, the sum of our three numbers should be: 1017
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1017.
Solution 1:
339, 339, 339
Verification:
(339 + 339 + 339) / 3 = 1017 / 3 ≈ 339
This solution is correct!
Solution 2:
339, 339, 339
Verification:
(339 + 339 + 339) / 3 = 1017 / 3 ≈ 339
This solution is correct!
Solution 3:
681, 311, 25
Verification:
(681 + 311 + 25) / 3 = 1017 / 3 ≈ 339
This solution is correct!
Solution 4:
977, 34, 6
Verification:
(977 + 34 + 6) / 3 = 1017 / 3 ≈ 339
This solution is correct!
Solution 5:
919, 96, 2
Verification:
(919 + 96 + 2) / 3 = 1017 / 3 ≈ 339
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 1017 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.