What three numbers have an average of 447?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 447. This means if we add these three numbers together and divide by 3, we should get 447.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 447 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 447 * 3 = x + y + z
- So, the sum of our three numbers should be: 1341
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1341.
Solution 1:
447, 447, 447
Verification:
(447 + 447 + 447) / 3 = 1341 / 3 ≈ 447
This solution is correct!
Solution 2:
447, 447, 447
Verification:
(447 + 447 + 447) / 3 = 1341 / 3 ≈ 447
This solution is correct!
Solution 3:
1306, 24, 11
Verification:
(1306 + 24 + 11) / 3 = 1341 / 3 ≈ 447
This solution is correct!
Solution 4:
936, 131, 274
Verification:
(936 + 131 + 274) / 3 = 1341 / 3 ≈ 447
This solution is correct!
Solution 5:
545, 567, 229
Verification:
(545 + 567 + 229) / 3 = 1341 / 3 ≈ 447
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 1341 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.