What three numbers have an average of 397?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 397. This means if we add these three numbers together and divide by 3, we should get 397.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 397 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 397 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 1191

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 1191.

Solution 1:

397, 397, 397

Verification:

(397 + 397 + 397) / 3 = 1191 / 3 ≈ 397

This solution is correct!

Solution 2:

397, 397, 397

Verification:

(397 + 397 + 397) / 3 = 1191 / 3 ≈ 397

This solution is correct!

Solution 3:

1185, 3, 3

Verification:

(1185 + 3 + 3) / 3 = 1191 / 3 ≈ 397

This solution is correct!

Solution 4:

1187, 1, 3

Verification:

(1187 + 1 + 3) / 3 = 1191 / 3 ≈ 397

This solution is correct!

Solution 5:

221, 826, 144

Verification:

(221 + 826 + 144) / 3 = 1191 / 3 ≈ 397

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 = 66What three numbers have an average of 66 ?
(X+Y+Z) / 3 = 137What three numbers have an average of 137 ?
(X+Y+Z) / 3 = 685What three numbers have an average of 685 ?

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