What three numbers have an average of 14?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 14. This means if we add these three numbers together and divide by 3, we should get 14.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 14 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 14 * 3 = x + y + z
- So, the sum of our three numbers should be: 42
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 42.
Solution 1:
14, 14, 14
Verification:
(14 + 14 + 14) / 3 = 42 / 3 ≈ 14
This solution is correct!
Solution 2:
14, 14, 14
Verification:
(14 + 14 + 14) / 3 = 42 / 3 ≈ 14
This solution is correct!
Solution 3:
7, 25, 10
Verification:
(7 + 25 + 10) / 3 = 42 / 3 ≈ 14
This solution is correct!
Solution 4:
6, 19, 17
Verification:
(6 + 19 + 17) / 3 = 42 / 3 ≈ 14
This solution is correct!
Solution 5:
24, 1, 17
Verification:
(24 + 1 + 17) / 3 = 42 / 3 ≈ 14
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 42 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.