What three numbers have an average of 311?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 311. This means if we add these three numbers together and divide by 3, we should get 311.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 311 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 311 * 3 = x + y + z
- So, the sum of our three numbers should be: 933
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 933.
Solution 1:
311, 311, 311
Verification:
(311 + 311 + 311) / 3 = 933 / 3 ≈ 311
This solution is correct!
Solution 2:
311, 311, 311
Verification:
(311 + 311 + 311) / 3 = 933 / 3 ≈ 311
This solution is correct!
Solution 3:
102, 812, 19
Verification:
(102 + 812 + 19) / 3 = 933 / 3 ≈ 311
This solution is correct!
Solution 4:
179, 454, 300
Verification:
(179 + 454 + 300) / 3 = 933 / 3 ≈ 311
This solution is correct!
Solution 5:
666, 224, 43
Verification:
(666 + 224 + 43) / 3 = 933 / 3 ≈ 311
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 933 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.