What three numbers have an average of 16?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 16. This means if we add these three numbers together and divide by 3, we should get 16.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 16 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 16 * 3 = x + y + z
- So, the sum of our three numbers should be: 48
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 48.
Solution 1:
16, 16, 16
Verification:
(16 + 16 + 16) / 3 = 48 / 3 ≈ 16
This solution is correct!
Solution 2:
16, 16, 16
Verification:
(16 + 16 + 16) / 3 = 48 / 3 ≈ 16
This solution is correct!
Solution 3:
16, 30, 2
Verification:
(16 + 30 + 2) / 3 = 48 / 3 ≈ 16
This solution is correct!
Solution 4:
16, 27, 5
Verification:
(16 + 27 + 5) / 3 = 48 / 3 ≈ 16
This solution is correct!
Solution 5:
37, 1, 10
Verification:
(37 + 1 + 10) / 3 = 48 / 3 ≈ 16
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 48 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.