What three numbers have an average of 227?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 227. This means if we add these three numbers together and divide by 3, we should get 227.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 227 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 227 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 681

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 681.

Solution 1:

227, 227, 227

Verification:

(227 + 227 + 227) / 3 = 681 / 3 ≈ 227

This solution is correct!

Solution 2:

227, 227, 227

Verification:

(227 + 227 + 227) / 3 = 681 / 3 ≈ 227

This solution is correct!

Solution 3:

408, 149, 124

Verification:

(408 + 149 + 124) / 3 = 681 / 3 ≈ 227

This solution is correct!

Solution 4:

158, 5, 518

Verification:

(158 + 5 + 518) / 3 = 681 / 3 ≈ 227

This solution is correct!

Solution 5:

256, 378, 47

Verification:

(256 + 378 + 47) / 3 = 681 / 3 ≈ 227

This solution is correct!

Explanation:

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

Remember:

Try it out:

(X+Y+Z) / 3 = 931What three numbers have an average of 931 ?
(X+Y+Z) / 3 = 833What three numbers have an average of 833 ?
(X+Y+Z) / 3 = 663What three numbers have an average of 663 ?

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