What three numbers have an average of 655?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 655. This means if we add these three numbers together and divide by 3, we should get 655.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 655 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 655 * 3 = x + y + z
- So, the sum of our three numbers should be: 1965
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1965.
Solution 1:
655, 655, 655
Verification:
(655 + 655 + 655) / 3 = 1965 / 3 ≈ 655
This solution is correct!
Solution 2:
655, 655, 655
Verification:
(655 + 655 + 655) / 3 = 1965 / 3 ≈ 655
This solution is correct!
Solution 3:
743, 999, 223
Verification:
(743 + 999 + 223) / 3 = 1965 / 3 ≈ 655
This solution is correct!
Solution 4:
403, 100, 1462
Verification:
(403 + 100 + 1462) / 3 = 1965 / 3 ≈ 655
This solution is correct!
Solution 5:
66, 1548, 351
Verification:
(66 + 1548 + 351) / 3 = 1965 / 3 ≈ 655
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 1965 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.