What three numbers have an average of 394?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 394. This means if we add these three numbers together and divide by 3, we should get 394.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 394 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 394 * 3 = x + y + z
- So, the sum of our three numbers should be: 1182
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1182.
Solution 1:
394, 394, 394
Verification:
(394 + 394 + 394) / 3 = 1182 / 3 ≈ 394
This solution is correct!
Solution 2:
394, 394, 394
Verification:
(394 + 394 + 394) / 3 = 1182 / 3 ≈ 394
This solution is correct!
Solution 3:
15, 1089, 78
Verification:
(15 + 1089 + 78) / 3 = 1182 / 3 ≈ 394
This solution is correct!
Solution 4:
756, 409, 17
Verification:
(756 + 409 + 17) / 3 = 1182 / 3 ≈ 394
This solution is correct!
Solution 5:
269, 851, 62
Verification:
(269 + 851 + 62) / 3 = 1182 / 3 ≈ 394
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 1182 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.