What three numbers have an average of 45?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 45. This means if we add these three numbers together and divide by 3, we should get 45.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 45 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 45 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 135

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 135.

Solution 1:

45, 45, 45

Verification:

(45 + 45 + 45) / 3 = 135 / 3 ≈ 45

This solution is correct!

Solution 2:

45, 45, 45

Verification:

(45 + 45 + 45) / 3 = 135 / 3 ≈ 45

This solution is correct!

Solution 3:

130, 1, 4

Verification:

(130 + 1 + 4) / 3 = 135 / 3 ≈ 45

This solution is correct!

Solution 4:

2, 51, 82

Verification:

(2 + 51 + 82) / 3 = 135 / 3 ≈ 45

This solution is correct!

Solution 5:

65, 62, 8

Verification:

(65 + 62 + 8) / 3 = 135 / 3 ≈ 45

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 = 58What three numbers have an average of 58 ?
(X+Y+Z) / 3 = 128What three numbers have an average of 128 ?
(X+Y+Z) / 3 = 560What three numbers have an average of 560 ?

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