What three numbers have an average of 413?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 413. This means if we add these three numbers together and divide by 3, we should get 413.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 413 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 413 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 1239

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 1239.

Solution 1:

413, 413, 413

Verification:

(413 + 413 + 413) / 3 = 1239 / 3 ≈ 413

This solution is correct!

Solution 2:

413, 413, 413

Verification:

(413 + 413 + 413) / 3 = 1239 / 3 ≈ 413

This solution is correct!

Solution 3:

1034, 129, 76

Verification:

(1034 + 129 + 76) / 3 = 1239 / 3 ≈ 413

This solution is correct!

Solution 4:

114, 405, 720

Verification:

(114 + 405 + 720) / 3 = 1239 / 3 ≈ 413

This solution is correct!

Solution 5:

984, 186, 69

Verification:

(984 + 186 + 69) / 3 = 1239 / 3 ≈ 413

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 = 367What three numbers have an average of 367 ?
(X+Y+Z) / 3 = 218What three numbers have an average of 218 ?
(X+Y+Z) / 3 = 105What three numbers have an average of 105 ?

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