What three numbers have an average of 209?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 209. This means if we add these three numbers together and divide by 3, we should get 209.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 209 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 209 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 627

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 627.

Solution 1:

209, 209, 209

Verification:

(209 + 209 + 209) / 3 = 627 / 3 ≈ 209

This solution is correct!

Solution 2:

209, 209, 209

Verification:

(209 + 209 + 209) / 3 = 627 / 3 ≈ 209

This solution is correct!

Solution 3:

500, 3, 124

Verification:

(500 + 3 + 124) / 3 = 627 / 3 ≈ 209

This solution is correct!

Solution 4:

588, 38, 1

Verification:

(588 + 38 + 1) / 3 = 627 / 3 ≈ 209

This solution is correct!

Solution 5:

348, 243, 36

Verification:

(348 + 243 + 36) / 3 = 627 / 3 ≈ 209

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 = 54What three numbers have an average of 54 ?
(X+Y+Z) / 3 = 365What three numbers have an average of 365 ?
(X+Y+Z) / 3 = 209What three numbers have an average of 209 ?

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