What three numbers have an average of 128?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 128. This means if we add these three numbers together and divide by 3, we should get 128.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 128 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 128 * 3 = x + y + z
- So, the sum of our three numbers should be: 384
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 384.
Solution 1:
128, 128, 128
Verification:
(128 + 128 + 128) / 3 = 384 / 3 ≈ 128
This solution is correct!
Solution 2:
128, 128, 128
Verification:
(128 + 128 + 128) / 3 = 384 / 3 ≈ 128
This solution is correct!
Solution 3:
314, 26, 44
Verification:
(314 + 26 + 44) / 3 = 384 / 3 ≈ 128
This solution is correct!
Solution 4:
256, 65, 63
Verification:
(256 + 65 + 63) / 3 = 384 / 3 ≈ 128
This solution is correct!
Solution 5:
367, 8, 9
Verification:
(367 + 8 + 9) / 3 = 384 / 3 ≈ 128
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 384 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.