What three numbers have an average of 317?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 317. This means if we add these three numbers together and divide by 3, we should get 317.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 317 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 317 * 3 = x + y + z
- So, the sum of our three numbers should be: 951
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 951.
Solution 1:
317, 317, 317
Verification:
(317 + 317 + 317) / 3 = 951 / 3 ≈ 317
This solution is correct!
Solution 2:
317, 317, 317
Verification:
(317 + 317 + 317) / 3 = 951 / 3 ≈ 317
This solution is correct!
Solution 3:
722, 159, 70
Verification:
(722 + 159 + 70) / 3 = 951 / 3 ≈ 317
This solution is correct!
Solution 4:
678, 271, 2
Verification:
(678 + 271 + 2) / 3 = 951 / 3 ≈ 317
This solution is correct!
Solution 5:
802, 107, 42
Verification:
(802 + 107 + 42) / 3 = 951 / 3 ≈ 317
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 951 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.