What three numbers have an average of 27?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 27. This means if we add these three numbers together and divide by 3, we should get 27.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 27 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 27 * 3 = x + y + z
- So, the sum of our three numbers should be: 81
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 81.
Solution 1:
27, 27, 27
Verification:
(27 + 27 + 27) / 3 = 81 / 3 ≈ 27
This solution is correct!
Solution 2:
27, 27, 27
Verification:
(27 + 27 + 27) / 3 = 81 / 3 ≈ 27
This solution is correct!
Solution 3:
34, 37, 10
Verification:
(34 + 37 + 10) / 3 = 81 / 3 ≈ 27
This solution is correct!
Solution 4:
42, 33, 6
Verification:
(42 + 33 + 6) / 3 = 81 / 3 ≈ 27
This solution is correct!
Solution 5:
12, 8, 61
Verification:
(12 + 8 + 61) / 3 = 81 / 3 ≈ 27
This solution is correct!
Explanation:
As you can see, there are many possible solutions. We can find more by:
- Choosing any two numbers
- Subtracting their sum from 81 to get the third number
Remember:
- The numbers don't have to be whole numbers.
- They can even be negative (although that might not make sense in some real-world contexts).
- The order of the numbers doesn't matter for the average.