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:
590, 266, 107
Verification:
(590 + 266 + 107) / 3 = 963 / 3 ≈ 321
This solution is correct!
Solution 4:
580, 254, 129
Verification:
(580 + 254 + 129) / 3 = 963 / 3 ≈ 321
This solution is correct!
Solution 5:
429, 40, 494
Verification:
(429 + 40 + 494) / 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.