What three numbers have an average of 414?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 414. This means if we add these three numbers together and divide by 3, we should get 414.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 414 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 414 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 1242

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 1242.

Solution 1:

414, 414, 414

Verification:

(414 + 414 + 414) / 3 = 1242 / 3 ≈ 414

This solution is correct!

Solution 2:

414, 414, 414

Verification:

(414 + 414 + 414) / 3 = 1242 / 3 ≈ 414

This solution is correct!

Solution 3:

310, 852, 80

Verification:

(310 + 852 + 80) / 3 = 1242 / 3 ≈ 414

This solution is correct!

Solution 4:

84, 288, 870

Verification:

(84 + 288 + 870) / 3 = 1242 / 3 ≈ 414

This solution is correct!

Solution 5:

1029, 77, 136

Verification:

(1029 + 77 + 136) / 3 = 1242 / 3 ≈ 414

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 = 430What three numbers have an average of 430 ?
(X+Y+Z) / 3 = 701What three numbers have an average of 701 ?
(X+Y+Z) / 3 = 591What three numbers have an average of 591 ?

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