What three numbers have an average of 107?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 107. This means if we add these three numbers together and divide by 3, we should get 107.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 107 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 107 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 321

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 321.

Solution 1:

107, 107, 107

Verification:

(107 + 107 + 107) / 3 = 321 / 3 ≈ 107

This solution is correct!

Solution 2:

107, 107, 107

Verification:

(107 + 107 + 107) / 3 = 321 / 3 ≈ 107

This solution is correct!

Solution 3:

160, 58, 103

Verification:

(160 + 58 + 103) / 3 = 321 / 3 ≈ 107

This solution is correct!

Solution 4:

185, 2, 134

Verification:

(185 + 2 + 134) / 3 = 321 / 3 ≈ 107

This solution is correct!

Solution 5:

259, 59, 3

Verification:

(259 + 59 + 3) / 3 = 321 / 3 ≈ 107

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 = 830What three numbers have an average of 830 ?
(X+Y+Z) / 3 = 823What three numbers have an average of 823 ?
(X+Y+Z) / 3 = 708What three numbers have an average of 708 ?

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