What three numbers have an average of 512?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 512. This means if we add these three numbers together and divide by 3, we should get 512.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 512 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 512 * 3 = x + y + z
- So, the sum of our three numbers should be: 1536
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1536.
Solution 1:
512, 512, 512
Verification:
(512 + 512 + 512) / 3 = 1536 / 3 ≈ 512
This solution is correct!
Solution 2:
512, 512, 512
Verification:
(512 + 512 + 512) / 3 = 1536 / 3 ≈ 512
This solution is correct!
Solution 3:
343, 18, 1175
Verification:
(343 + 18 + 1175) / 3 = 1536 / 3 ≈ 512
This solution is correct!
Solution 4:
985, 75, 476
Verification:
(985 + 75 + 476) / 3 = 1536 / 3 ≈ 512
This solution is correct!
Solution 5:
292, 1089, 155
Verification:
(292 + 1089 + 155) / 3 = 1536 / 3 ≈ 512
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 1536 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.