What three numbers have an average of 409?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 409. This means if we add these three numbers together and divide by 3, we should get 409.

Step-by-step Solution:

1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
2. In this case: 409 = (x + y + z) / 3
3. To find the sum, multiply both sides by 3: 409 * 3 = x + y + z
4. So, the sum of our three numbers should be: 1227

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 1227.

Explanation:

As you can see, there are many possible solutions. We can find more by:

• Choosing any two numbers
• Subtracting their sum from 1227 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.