What three numbers have an average of 71?

Part 1: Understanding the Problem

We're looking for three numbers whose average is 71. This means if we add these three numbers together and divide by 3, we should get 71.

Step-by-step Solution:

  1. Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
  2. In this case: 71 = (x + y + z) / 3
  3. To find the sum, multiply both sides by 3: 71 * 3 = x + y + z
  4. So, the sum of our three numbers should be: 213

Part 2: Finding Solutions

Now, let's find multiple sets of three numbers that add up to 213.

Solution 1:

71, 71, 71

Verification:

(71 + 71 + 71) / 3 = 213 / 3 ≈ 71

This solution is correct!

Solution 2:

71, 71, 71

Verification:

(71 + 71 + 71) / 3 = 213 / 3 ≈ 71

This solution is correct!

Solution 3:

87, 19, 107

Verification:

(87 + 19 + 107) / 3 = 213 / 3 ≈ 71

This solution is correct!

Solution 4:

35, 61, 117

Verification:

(35 + 61 + 117) / 3 = 213 / 3 ≈ 71

This solution is correct!

Solution 5:

59, 81, 73

Verification:

(59 + 81 + 73) / 3 = 213 / 3 ≈ 71

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 = 431What three numbers have an average of 431 ?
(X+Y+Z) / 3 = 77What three numbers have an average of 77 ?
(X+Y+Z) / 3 = 427What three numbers have an average of 427 ?

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