What three numbers have an average of 108?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 108. This means if we add these three numbers together and divide by 3, we should get 108.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 108 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 108 * 3 = x + y + z
- So, the sum of our three numbers should be: 324
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 324.
Solution 1:
108, 108, 108
Verification:
(108 + 108 + 108) / 3 = 324 / 3 ≈ 108
This solution is correct!
Solution 2:
108, 108, 108
Verification:
(108 + 108 + 108) / 3 = 324 / 3 ≈ 108
This solution is correct!
Solution 3:
322, 1, 1
Verification:
(322 + 1 + 1) / 3 = 324 / 3 ≈ 108
This solution is correct!
Solution 4:
139, 78, 107
Verification:
(139 + 78 + 107) / 3 = 324 / 3 ≈ 108
This solution is correct!
Solution 5:
31, 190, 103
Verification:
(31 + 190 + 103) / 3 = 324 / 3 ≈ 108
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 324 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.