What three numbers have an average of 404?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 404. This means if we add these three numbers together and divide by 3, we should get 404.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 404 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 404 * 3 = x + y + z
- So, the sum of our three numbers should be: 1212
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1212.
Solution 1:
404, 404, 404
Verification:
(404 + 404 + 404) / 3 = 1212 / 3 ≈ 404
This solution is correct!
Solution 2:
404, 404, 404
Verification:
(404 + 404 + 404) / 3 = 1212 / 3 ≈ 404
This solution is correct!
Solution 3:
306, 873, 33
Verification:
(306 + 873 + 33) / 3 = 1212 / 3 ≈ 404
This solution is correct!
Solution 4:
727, 156, 329
Verification:
(727 + 156 + 329) / 3 = 1212 / 3 ≈ 404
This solution is correct!
Solution 5:
1017, 13, 182
Verification:
(1017 + 13 + 182) / 3 = 1212 / 3 ≈ 404
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 1212 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.