What three numbers have an average of 84?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 84. This means if we add these three numbers together and divide by 3, we should get 84.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 84 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 84 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 252

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 252.

Solution 1:

84, 84, 84

Verification:

(84 + 84 + 84) / 3 = 252 / 3 ≈ 84

This solution is correct!

Solution 2:

84, 84, 84

Verification:

(84 + 84 + 84) / 3 = 252 / 3 ≈ 84

This solution is correct!

Solution 3:

161, 50, 41

Verification:

(161 + 50 + 41) / 3 = 252 / 3 ≈ 84

This solution is correct!

Solution 4:

130, 36, 86

Verification:

(130 + 36 + 86) / 3 = 252 / 3 ≈ 84

This solution is correct!

Solution 5:

222, 14, 16

Verification:

(222 + 14 + 16) / 3 = 252 / 3 ≈ 84

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 = 318What three numbers have an average of 318 ?
(X+Y+Z) / 3 = 903What three numbers have an average of 903 ?
(X+Y+Z) / 3 = 290What three numbers have an average of 290 ?

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