What three numbers have an average of 831?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 831. This means if we add these three numbers together and divide by 3, we should get 831.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 831 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 831 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 2493

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 2493.

Solution 1:

831, 831, 831

Verification:

(831 + 831 + 831) / 3 = 2493 / 3 ≈ 831

This solution is correct!

Solution 2:

831, 831, 831

Verification:

(831 + 831 + 831) / 3 = 2493 / 3 ≈ 831

This solution is correct!

Solution 3:

1497, 302, 694

Verification:

(1497 + 302 + 694) / 3 = 2493 / 3 ≈ 831

This solution is correct!

Solution 4:

583, 1046, 864

Verification:

(583 + 1046 + 864) / 3 = 2493 / 3 ≈ 831

This solution is correct!

Solution 5:

91, 964, 1438

Verification:

(91 + 964 + 1438) / 3 = 2493 / 3 ≈ 831

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 = 321What three numbers have an average of 321 ?
(X+Y+Z) / 3 = 789What three numbers have an average of 789 ?
(X+Y+Z) / 3 = 584What three numbers have an average of 584 ?

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