What three numbers have an average of 83?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 83. This means if we add these three numbers together and divide by 3, we should get 83.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 83 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 83 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 249

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 249.

Solution 1:

83, 83, 83

Verification:

(83 + 83 + 83) / 3 = 249 / 3 ≈ 83

This solution is correct!

Solution 2:

83, 83, 83

Verification:

(83 + 83 + 83) / 3 = 249 / 3 ≈ 83

This solution is correct!

Solution 3:

126, 28, 95

Verification:

(126 + 28 + 95) / 3 = 249 / 3 ≈ 83

This solution is correct!

Solution 4:

84, 89, 76

Verification:

(84 + 89 + 76) / 3 = 249 / 3 ≈ 83

This solution is correct!

Solution 5:

80, 143, 26

Verification:

(80 + 143 + 26) / 3 = 249 / 3 ≈ 83

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 = 603What three numbers have an average of 603 ?
(X+Y+Z) / 3 = 989What three numbers have an average of 989 ?
(X+Y+Z) / 3 = 745What three numbers have an average of 745 ?

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