What three numbers have an average of 214?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 214. This means if we add these three numbers together and divide by 3, we should get 214.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 214 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 214 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 642

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 642.

Solution 1:

214, 214, 214

Verification:

(214 + 214 + 214) / 3 = 642 / 3 ≈ 214

This solution is correct!

Solution 2:

214, 214, 214

Verification:

(214 + 214 + 214) / 3 = 642 / 3 ≈ 214

This solution is correct!

Solution 3:

6, 602, 34

Verification:

(6 + 602 + 34) / 3 = 642 / 3 ≈ 214

This solution is correct!

Solution 4:

176, 191, 275

Verification:

(176 + 191 + 275) / 3 = 642 / 3 ≈ 214

This solution is correct!

Solution 5:

529, 8, 105

Verification:

(529 + 8 + 105) / 3 = 642 / 3 ≈ 214

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 = 186What three numbers have an average of 186 ?
(X+Y+Z) / 3 = 904What three numbers have an average of 904 ?
(X+Y+Z) / 3 = 936What three numbers have an average of 936 ?

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