What three numbers have an average of 619?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 619. This means if we add these three numbers together and divide by 3, we should get 619.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 619 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 619 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 1857

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 1857.

Solution 1:

619, 619, 619

Verification:

(619 + 619 + 619) / 3 = 1857 / 3 ≈ 619

This solution is correct!

Solution 2:

619, 619, 619

Verification:

(619 + 619 + 619) / 3 = 1857 / 3 ≈ 619

This solution is correct!

Solution 3:

1712, 65, 80

Verification:

(1712 + 65 + 80) / 3 = 1857 / 3 ≈ 619

This solution is correct!

Solution 4:

204, 1136, 517

Verification:

(204 + 1136 + 517) / 3 = 1857 / 3 ≈ 619

This solution is correct!

Solution 5:

393, 375, 1089

Verification:

(393 + 375 + 1089) / 3 = 1857 / 3 ≈ 619

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 = 167What three numbers have an average of 167 ?
(X+Y+Z) / 3 = 898What three numbers have an average of 898 ?
(X+Y+Z) / 3 = 45What three numbers have an average of 45 ?

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