What three numbers have an average of 347?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 347. This means if we add these three numbers together and divide by 3, we should get 347.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 347 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 347 * 3 = x + y + z
- So, the sum of our three numbers should be: 1041
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1041.
Solution 1:
347, 347, 347
Verification:
(347 + 347 + 347) / 3 = 1041 / 3 ≈ 347
This solution is correct!
Solution 2:
347, 347, 347
Verification:
(347 + 347 + 347) / 3 = 1041 / 3 ≈ 347
This solution is correct!
Solution 3:
343, 11, 687
Verification:
(343 + 11 + 687) / 3 = 1041 / 3 ≈ 347
This solution is correct!
Solution 4:
536, 162, 343
Verification:
(536 + 162 + 343) / 3 = 1041 / 3 ≈ 347
This solution is correct!
Solution 5:
43, 729, 269
Verification:
(43 + 729 + 269) / 3 = 1041 / 3 ≈ 347
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 1041 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.