What three numbers have an average of 309?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 309. This means if we add these three numbers together and divide by 3, we should get 309.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 309 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 309 * 3 = x + y + z
- So, the sum of our three numbers should be: 927
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 927.
Solution 1:
309, 309, 309
Verification:
(309 + 309 + 309) / 3 = 927 / 3 ≈ 309
This solution is correct!
Solution 2:
309, 309, 309
Verification:
(309 + 309 + 309) / 3 = 927 / 3 ≈ 309
This solution is correct!
Solution 3:
632, 173, 122
Verification:
(632 + 173 + 122) / 3 = 927 / 3 ≈ 309
This solution is correct!
Solution 4:
213, 97, 617
Verification:
(213 + 97 + 617) / 3 = 927 / 3 ≈ 309
This solution is correct!
Solution 5:
613, 312, 2
Verification:
(613 + 312 + 2) / 3 = 927 / 3 ≈ 309
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 927 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.