What three numbers have an average of 38?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 38. This means if we add these three numbers together and divide by 3, we should get 38.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 38 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 38 * 3 = x + y + z
- So, the sum of our three numbers should be: 114
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 114.
Solution 1:
38, 38, 38
Verification:
(38 + 38 + 38) / 3 = 114 / 3 ≈ 38
This solution is correct!
Solution 2:
38, 38, 38
Verification:
(38 + 38 + 38) / 3 = 114 / 3 ≈ 38
This solution is correct!
Solution 3:
97, 6, 11
Verification:
(97 + 6 + 11) / 3 = 114 / 3 ≈ 38
This solution is correct!
Solution 4:
75, 19, 20
Verification:
(75 + 19 + 20) / 3 = 114 / 3 ≈ 38
This solution is correct!
Solution 5:
20, 75, 19
Verification:
(20 + 75 + 19) / 3 = 114 / 3 ≈ 38
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 114 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.