What three numbers have an average of 513?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 513. This means if we add these three numbers together and divide by 3, we should get 513.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 513 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 513 * 3 = x + y + z
- So, the sum of our three numbers should be: 1539
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1539.
Solution 1:
513, 513, 513
Verification:
(513 + 513 + 513) / 3 = 1539 / 3 ≈ 513
This solution is correct!
Solution 2:
513, 513, 513
Verification:
(513 + 513 + 513) / 3 = 1539 / 3 ≈ 513
This solution is correct!
Solution 3:
737, 128, 674
Verification:
(737 + 128 + 674) / 3 = 1539 / 3 ≈ 513
This solution is correct!
Solution 4:
618, 398, 523
Verification:
(618 + 398 + 523) / 3 = 1539 / 3 ≈ 513
This solution is correct!
Solution 5:
210, 1268, 61
Verification:
(210 + 1268 + 61) / 3 = 1539 / 3 ≈ 513
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 1539 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.