What three numbers have an average of 78?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 78. This means if we add these three numbers together and divide by 3, we should get 78.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 78 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 78 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 234

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 234.

Solution 1:

78, 78, 78

Verification:

(78 + 78 + 78) / 3 = 234 / 3 ≈ 78

This solution is correct!

Solution 2:

78, 78, 78

Verification:

(78 + 78 + 78) / 3 = 234 / 3 ≈ 78

This solution is correct!

Solution 3:

227, 5, 2

Verification:

(227 + 5 + 2) / 3 = 234 / 3 ≈ 78

This solution is correct!

Solution 4:

22, 102, 110

Verification:

(22 + 102 + 110) / 3 = 234 / 3 ≈ 78

This solution is correct!

Solution 5:

23, 90, 121

Verification:

(23 + 90 + 121) / 3 = 234 / 3 ≈ 78

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 = 659What three numbers have an average of 659 ?
(X+Y+Z) / 3 = 28What three numbers have an average of 28 ?
(X+Y+Z) / 3 = 692What three numbers have an average of 692 ?

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