What three numbers have an average of 327?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 327. This means if we add these three numbers together and divide by 3, we should get 327.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 327 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 327 * 3 = x + y + z
- So, the sum of our three numbers should be: 981
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 981.
Solution 1:
327, 327, 327
Verification:
(327 + 327 + 327) / 3 = 981 / 3 ≈ 327
This solution is correct!
Solution 2:
327, 327, 327
Verification:
(327 + 327 + 327) / 3 = 981 / 3 ≈ 327
This solution is correct!
Solution 3:
819, 151, 11
Verification:
(819 + 151 + 11) / 3 = 981 / 3 ≈ 327
This solution is correct!
Solution 4:
371, 127, 483
Verification:
(371 + 127 + 483) / 3 = 981 / 3 ≈ 327
This solution is correct!
Solution 5:
398, 249, 334
Verification:
(398 + 249 + 334) / 3 = 981 / 3 ≈ 327
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 981 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.