What three numbers have an average of 41?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 41. This means if we add these three numbers together and divide by 3, we should get 41.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 41 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 41 * 3 = x + y + z
- So, the sum of our three numbers should be: 123
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 123.
Solution 1:
41, 41, 41
Verification:
(41 + 41 + 41) / 3 = 123 / 3 ≈ 41
This solution is correct!
Solution 2:
41, 41, 41
Verification:
(41 + 41 + 41) / 3 = 123 / 3 ≈ 41
This solution is correct!
Solution 3:
89, 30, 4
Verification:
(89 + 30 + 4) / 3 = 123 / 3 ≈ 41
This solution is correct!
Solution 4:
35, 47, 41
Verification:
(35 + 47 + 41) / 3 = 123 / 3 ≈ 41
This solution is correct!
Solution 5:
38, 60, 25
Verification:
(38 + 60 + 25) / 3 = 123 / 3 ≈ 41
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 123 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.