What three numbers have an average of 490?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 490. This means if we add these three numbers together and divide by 3, we should get 490.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 490 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 490 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 1470

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 1470.

Solution 1:

490, 490, 490

Verification:

(490 + 490 + 490) / 3 = 1470 / 3 ≈ 490

This solution is correct!

Solution 2:

490, 490, 490

Verification:

(490 + 490 + 490) / 3 = 1470 / 3 ≈ 490

This solution is correct!

Solution 3:

499, 611, 360

Verification:

(499 + 611 + 360) / 3 = 1470 / 3 ≈ 490

This solution is correct!

Solution 4:

1340, 125, 5

Verification:

(1340 + 125 + 5) / 3 = 1470 / 3 ≈ 490

This solution is correct!

Solution 5:

362, 65, 1043

Verification:

(362 + 65 + 1043) / 3 = 1470 / 3 ≈ 490

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 = 205What three numbers have an average of 205 ?
(X+Y+Z) / 3 = 291What three numbers have an average of 291 ?
(X+Y+Z) / 3 = 69What three numbers have an average of 69 ?

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