What three numbers have an average of 519?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 519. This means if we add these three numbers together and divide by 3, we should get 519.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 519 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 519 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 1557

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 1557.

Solution 1:

519, 519, 519

Verification:

(519 + 519 + 519) / 3 = 1557 / 3 ≈ 519

This solution is correct!

Solution 2:

519, 519, 519

Verification:

(519 + 519 + 519) / 3 = 1557 / 3 ≈ 519

This solution is correct!

Solution 3:

440, 912, 205

Verification:

(440 + 912 + 205) / 3 = 1557 / 3 ≈ 519

This solution is correct!

Solution 4:

889, 410, 258

Verification:

(889 + 410 + 258) / 3 = 1557 / 3 ≈ 519

This solution is correct!

Solution 5:

136, 56, 1365

Verification:

(136 + 56 + 1365) / 3 = 1557 / 3 ≈ 519

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 = 232What three numbers have an average of 232 ?
(X+Y+Z) / 3 = 98What three numbers have an average of 98 ?
(X+Y+Z) / 3 = 230What three numbers have an average of 230 ?

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