What three numbers have an average of 441?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 441. This means if we add these three numbers together and divide by 3, we should get 441.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 441 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 441 * 3 = x + y + z
- So, the sum of our three numbers should be: 1323
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1323.
Solution 1:
441, 441, 441
Verification:
(441 + 441 + 441) / 3 = 1323 / 3 ≈ 441
This solution is correct!
Solution 2:
441, 441, 441
Verification:
(441 + 441 + 441) / 3 = 1323 / 3 ≈ 441
This solution is correct!
Solution 3:
282, 595, 446
Verification:
(282 + 595 + 446) / 3 = 1323 / 3 ≈ 441
This solution is correct!
Solution 4:
1076, 37, 210
Verification:
(1076 + 37 + 210) / 3 = 1323 / 3 ≈ 441
This solution is correct!
Solution 5:
461, 327, 535
Verification:
(461 + 327 + 535) / 3 = 1323 / 3 ≈ 441
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 1323 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.