What three numbers have an average of 392?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 392. This means if we add these three numbers together and divide by 3, we should get 392.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 392 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 392 * 3 = x + y + z
- So, the sum of our three numbers should be: 1176
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1176.
Solution 1:
392, 392, 392
Verification:
(392 + 392 + 392) / 3 = 1176 / 3 ≈ 392
This solution is correct!
Solution 2:
392, 392, 392
Verification:
(392 + 392 + 392) / 3 = 1176 / 3 ≈ 392
This solution is correct!
Solution 3:
353, 193, 630
Verification:
(353 + 193 + 630) / 3 = 1176 / 3 ≈ 392
This solution is correct!
Solution 4:
123, 155, 898
Verification:
(123 + 155 + 898) / 3 = 1176 / 3 ≈ 392
This solution is correct!
Solution 5:
522, 514, 140
Verification:
(522 + 514 + 140) / 3 = 1176 / 3 ≈ 392
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 1176 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.