What three numbers have an average of 313?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 313. This means if we add these three numbers together and divide by 3, we should get 313.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 313 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 313 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 939

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 939.

Solution 1:

313, 313, 313

Verification:

(313 + 313 + 313) / 3 = 939 / 3 ≈ 313

This solution is correct!

Solution 2:

313, 313, 313

Verification:

(313 + 313 + 313) / 3 = 939 / 3 ≈ 313

This solution is correct!

Solution 3:

371, 76, 492

Verification:

(371 + 76 + 492) / 3 = 939 / 3 ≈ 313

This solution is correct!

Solution 4:

520, 287, 132

Verification:

(520 + 287 + 132) / 3 = 939 / 3 ≈ 313

This solution is correct!

Solution 5:

142, 283, 514

Verification:

(142 + 283 + 514) / 3 = 939 / 3 ≈ 313

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 = 247What three numbers have an average of 247 ?
(X+Y+Z) / 3 = 403What three numbers have an average of 403 ?
(X+Y+Z) / 3 = 547What three numbers have an average of 547 ?

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