What three numbers have an average of 256?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 256. This means if we add these three numbers together and divide by 3, we should get 256.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 256 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 256 * 3 = x + y + z
- So, the sum of our three numbers should be: 768
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 768.
Solution 1:
256, 256, 256
Verification:
(256 + 256 + 256) / 3 = 768 / 3 ≈ 256
This solution is correct!
Solution 2:
256, 256, 256
Verification:
(256 + 256 + 256) / 3 = 768 / 3 ≈ 256
This solution is correct!
Solution 3:
512, 46, 210
Verification:
(512 + 46 + 210) / 3 = 768 / 3 ≈ 256
This solution is correct!
Solution 4:
143, 272, 353
Verification:
(143 + 272 + 353) / 3 = 768 / 3 ≈ 256
This solution is correct!
Solution 5:
31, 612, 125
Verification:
(31 + 612 + 125) / 3 = 768 / 3 ≈ 256
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 768 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.