What three numbers have an average of 344?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 344. This means if we add these three numbers together and divide by 3, we should get 344.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 344 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 344 * 3 = x + y + z
- So, the sum of our three numbers should be: 1032
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1032.
Solution 1:
344, 344, 344
Verification:
(344 + 344 + 344) / 3 = 1032 / 3 ≈ 344
This solution is correct!
Solution 2:
344, 344, 344
Verification:
(344 + 344 + 344) / 3 = 1032 / 3 ≈ 344
This solution is correct!
Solution 3:
474, 4, 554
Verification:
(474 + 4 + 554) / 3 = 1032 / 3 ≈ 344
This solution is correct!
Solution 4:
217, 240, 575
Verification:
(217 + 240 + 575) / 3 = 1032 / 3 ≈ 344
This solution is correct!
Solution 5:
334, 189, 509
Verification:
(334 + 189 + 509) / 3 = 1032 / 3 ≈ 344
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 1032 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.