What three numbers have an average of 77?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 77. This means if we add these three numbers together and divide by 3, we should get 77.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 77 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 77 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 231

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 231.

Solution 1:

77, 77, 77

Verification:

(77 + 77 + 77) / 3 = 231 / 3 ≈ 77

This solution is correct!

Solution 2:

77, 77, 77

Verification:

(77 + 77 + 77) / 3 = 231 / 3 ≈ 77

This solution is correct!

Solution 3:

89, 132, 10

Verification:

(89 + 132 + 10) / 3 = 231 / 3 ≈ 77

This solution is correct!

Solution 4:

226, 2, 3

Verification:

(226 + 2 + 3) / 3 = 231 / 3 ≈ 77

This solution is correct!

Solution 5:

226, 4, 1

Verification:

(226 + 4 + 1) / 3 = 231 / 3 ≈ 77

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 = 937What three numbers have an average of 937 ?
(X+Y+Z) / 3 = 954What three numbers have an average of 954 ?
(X+Y+Z) / 3 = 538What three numbers have an average of 538 ?

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