What three numbers have an average of 412?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 412. This means if we add these three numbers together and divide by 3, we should get 412.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 412 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 412 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 1236

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 1236.

Solution 1:

412, 412, 412

Verification:

(412 + 412 + 412) / 3 = 1236 / 3 ≈ 412

This solution is correct!

Solution 2:

412, 412, 412

Verification:

(412 + 412 + 412) / 3 = 1236 / 3 ≈ 412

This solution is correct!

Solution 3:

1125, 85, 26

Verification:

(1125 + 85 + 26) / 3 = 1236 / 3 ≈ 412

This solution is correct!

Solution 4:

229, 591, 416

Verification:

(229 + 591 + 416) / 3 = 1236 / 3 ≈ 412

This solution is correct!

Solution 5:

191, 912, 133

Verification:

(191 + 912 + 133) / 3 = 1236 / 3 ≈ 412

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 = 854What three numbers have an average of 854 ?
(X+Y+Z) / 3 = 846What three numbers have an average of 846 ?
(X+Y+Z) / 3 = 928What three numbers have an average of 928 ?

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