What three numbers have an average of 195?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 195. This means if we add these three numbers together and divide by 3, we should get 195.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 195 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 195 * 3 = x + y + z
- So, the sum of our three numbers should be: 585
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 585.
Solution 1:
195, 195, 195
Verification:
(195 + 195 + 195) / 3 = 585 / 3 ≈ 195
This solution is correct!
Solution 2:
195, 195, 195
Verification:
(195 + 195 + 195) / 3 = 585 / 3 ≈ 195
This solution is correct!
Solution 3:
121, 43, 421
Verification:
(121 + 43 + 421) / 3 = 585 / 3 ≈ 195
This solution is correct!
Solution 4:
44, 224, 317
Verification:
(44 + 224 + 317) / 3 = 585 / 3 ≈ 195
This solution is correct!
Solution 5:
547, 5, 33
Verification:
(547 + 5 + 33) / 3 = 585 / 3 ≈ 195
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 585 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.