What three numbers have an average of 241?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 241. This means if we add these three numbers together and divide by 3, we should get 241.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 241 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 241 * 3 = x + y + z
- So, the sum of our three numbers should be: 723
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 723.
Solution 1:
241, 241, 241
Verification:
(241 + 241 + 241) / 3 = 723 / 3 ≈ 241
This solution is correct!
Solution 2:
241, 241, 241
Verification:
(241 + 241 + 241) / 3 = 723 / 3 ≈ 241
This solution is correct!
Solution 3:
560, 114, 49
Verification:
(560 + 114 + 49) / 3 = 723 / 3 ≈ 241
This solution is correct!
Solution 4:
386, 276, 61
Verification:
(386 + 276 + 61) / 3 = 723 / 3 ≈ 241
This solution is correct!
Solution 5:
216, 264, 243
Verification:
(216 + 264 + 243) / 3 = 723 / 3 ≈ 241
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 723 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.