What three numbers have an average of 331?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 331. This means if we add these three numbers together and divide by 3, we should get 331.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 331 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 331 * 3 = x + y + z
- So, the sum of our three numbers should be: 993
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 993.
Solution 1:
331, 331, 331
Verification:
(331 + 331 + 331) / 3 = 993 / 3 ≈ 331
This solution is correct!
Solution 2:
331, 331, 331
Verification:
(331 + 331 + 331) / 3 = 993 / 3 ≈ 331
This solution is correct!
Solution 3:
210, 14, 769
Verification:
(210 + 14 + 769) / 3 = 993 / 3 ≈ 331
This solution is correct!
Solution 4:
541, 281, 171
Verification:
(541 + 281 + 171) / 3 = 993 / 3 ≈ 331
This solution is correct!
Solution 5:
859, 83, 51
Verification:
(859 + 83 + 51) / 3 = 993 / 3 ≈ 331
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 993 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.