What three numbers have an average of 364?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 364. This means if we add these three numbers together and divide by 3, we should get 364.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 364 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 364 * 3 = x + y + z
- So, the sum of our three numbers should be: 1092
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1092.
Solution 1:
364, 364, 364
Verification:
(364 + 364 + 364) / 3 = 1092 / 3 ≈ 364
This solution is correct!
Solution 2:
364, 364, 364
Verification:
(364 + 364 + 364) / 3 = 1092 / 3 ≈ 364
This solution is correct!
Solution 3:
591, 67, 434
Verification:
(591 + 67 + 434) / 3 = 1092 / 3 ≈ 364
This solution is correct!
Solution 4:
799, 119, 174
Verification:
(799 + 119 + 174) / 3 = 1092 / 3 ≈ 364
This solution is correct!
Solution 5:
36, 941, 115
Verification:
(36 + 941 + 115) / 3 = 1092 / 3 ≈ 364
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 1092 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.