What three numbers have an average of 17?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 17. This means if we add these three numbers together and divide by 3, we should get 17.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 17 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 17 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 51

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 51.

Solution 1:

17, 17, 17

Verification:

(17 + 17 + 17) / 3 = 51 / 3 ≈ 17

This solution is correct!

Solution 2:

17, 17, 17

Verification:

(17 + 17 + 17) / 3 = 51 / 3 ≈ 17

This solution is correct!

Solution 3:

36, 7, 8

Verification:

(36 + 7 + 8) / 3 = 51 / 3 ≈ 17

This solution is correct!

Solution 4:

3, 3, 45

Verification:

(3 + 3 + 45) / 3 = 51 / 3 ≈ 17

This solution is correct!

Solution 5:

46, 2, 3

Verification:

(46 + 2 + 3) / 3 = 51 / 3 ≈ 17

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 = 36What three numbers have an average of 36 ?
(X+Y+Z) / 3 = 812What three numbers have an average of 812 ?
(X+Y+Z) / 3 = 712What three numbers have an average of 712 ?

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