What three numbers have an average of 138?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 138. This means if we add these three numbers together and divide by 3, we should get 138.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 138 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 138 * 3 = x + y + z
- So, the sum of our three numbers should be: 414
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 414.
Solution 1:
138, 138, 138
Verification:
(138 + 138 + 138) / 3 = 414 / 3 ≈ 138
This solution is correct!
Solution 2:
138, 138, 138
Verification:
(138 + 138 + 138) / 3 = 414 / 3 ≈ 138
This solution is correct!
Solution 3:
22, 353, 39
Verification:
(22 + 353 + 39) / 3 = 414 / 3 ≈ 138
This solution is correct!
Solution 4:
309, 37, 68
Verification:
(309 + 37 + 68) / 3 = 414 / 3 ≈ 138
This solution is correct!
Solution 5:
296, 14, 104
Verification:
(296 + 14 + 104) / 3 = 414 / 3 ≈ 138
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 414 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.