What three numbers have an average of 75?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 75. This means if we add these three numbers together and divide by 3, we should get 75.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 75 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 75 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 225

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 225.

Solution 1:

75, 75, 75

Verification:

(75 + 75 + 75) / 3 = 225 / 3 ≈ 75

This solution is correct!

Solution 2:

75, 75, 75

Verification:

(75 + 75 + 75) / 3 = 225 / 3 ≈ 75

This solution is correct!

Solution 3:

200, 5, 20

Verification:

(200 + 5 + 20) / 3 = 225 / 3 ≈ 75

This solution is correct!

Solution 4:

92, 104, 29

Verification:

(92 + 104 + 29) / 3 = 225 / 3 ≈ 75

This solution is correct!

Solution 5:

8, 108, 109

Verification:

(8 + 108 + 109) / 3 = 225 / 3 ≈ 75

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 = 213What three numbers have an average of 213 ?
(X+Y+Z) / 3 = 531What three numbers have an average of 531 ?
(X+Y+Z) / 3 = 587What three numbers have an average of 587 ?

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