What three numbers have an average of 321?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 321. This means if we add these three numbers together and divide by 3, we should get 321.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 321 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 321 * 3 = x + y + z
- So, the sum of our three numbers should be: 963
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 963.
Solution 1:
321, 321, 321
Verification:
(321 + 321 + 321) / 3 = 963 / 3 ≈ 321
This solution is correct!
Solution 2:
321, 321, 321
Verification:
(321 + 321 + 321) / 3 = 963 / 3 ≈ 321
This solution is correct!
Solution 3:
616, 56, 291
Verification:
(616 + 56 + 291) / 3 = 963 / 3 ≈ 321
This solution is correct!
Solution 4:
328, 462, 173
Verification:
(328 + 462 + 173) / 3 = 963 / 3 ≈ 321
This solution is correct!
Solution 5:
848, 114, 1
Verification:
(848 + 114 + 1) / 3 = 963 / 3 ≈ 321
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 963 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.