What three numbers have an average of 493?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 493. This means if we add these three numbers together and divide by 3, we should get 493.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 493 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 493 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 1479

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 1479.

Solution 1:

493, 493, 493

Verification:

(493 + 493 + 493) / 3 = 1479 / 3 ≈ 493

This solution is correct!

Solution 2:

493, 493, 493

Verification:

(493 + 493 + 493) / 3 = 1479 / 3 ≈ 493

This solution is correct!

Solution 3:

166, 652, 661

Verification:

(166 + 652 + 661) / 3 = 1479 / 3 ≈ 493

This solution is correct!

Solution 4:

1001, 284, 194

Verification:

(1001 + 284 + 194) / 3 = 1479 / 3 ≈ 493

This solution is correct!

Solution 5:

875, 114, 490

Verification:

(875 + 114 + 490) / 3 = 1479 / 3 ≈ 493

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 = 26What three numbers have an average of 26 ?
(X+Y+Z) / 3 = 840What three numbers have an average of 840 ?
(X+Y+Z) / 3 = 299What three numbers have an average of 299 ?

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