What three numbers have an average of 823?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 823. This means if we add these three numbers together and divide by 3, we should get 823.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 823 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 823 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 2469

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 2469.

Solution 1:

823, 823, 823

Verification:

(823 + 823 + 823) / 3 = 2469 / 3 ≈ 823

This solution is correct!

Solution 2:

823, 823, 823

Verification:

(823 + 823 + 823) / 3 = 2469 / 3 ≈ 823

This solution is correct!

Solution 3:

834, 500, 1135

Verification:

(834 + 500 + 1135) / 3 = 2469 / 3 ≈ 823

This solution is correct!

Solution 4:

778, 1537, 154

Verification:

(778 + 1537 + 154) / 3 = 2469 / 3 ≈ 823

This solution is correct!

Solution 5:

1222, 414, 833

Verification:

(1222 + 414 + 833) / 3 = 2469 / 3 ≈ 823

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 = 742What three numbers have an average of 742 ?
(X+Y+Z) / 3 = 157What three numbers have an average of 157 ?
(X+Y+Z) / 3 = 164What three numbers have an average of 164 ?

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