What three numbers have an average of 491?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 491. This means if we add these three numbers together and divide by 3, we should get 491.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 491 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 491 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 1473

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 1473.

Solution 1:

491, 491, 491

Verification:

(491 + 491 + 491) / 3 = 1473 / 3 ≈ 491

This solution is correct!

Solution 2:

491, 491, 491

Verification:

(491 + 491 + 491) / 3 = 1473 / 3 ≈ 491

This solution is correct!

Solution 3:

423, 611, 439

Verification:

(423 + 611 + 439) / 3 = 1473 / 3 ≈ 491

This solution is correct!

Solution 4:

1385, 76, 12

Verification:

(1385 + 76 + 12) / 3 = 1473 / 3 ≈ 491

This solution is correct!

Solution 5:

770, 564, 139

Verification:

(770 + 564 + 139) / 3 = 1473 / 3 ≈ 491

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 = 365What three numbers have an average of 365 ?
(X+Y+Z) / 3 = 497What three numbers have an average of 497 ?
(X+Y+Z) / 3 = 613What three numbers have an average of 613 ?

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