What three numbers have an average of 510?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 510. This means if we add these three numbers together and divide by 3, we should get 510.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 510 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 510 * 3 = x + y + z
- So, the sum of our three numbers should be: 1530
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1530.
Solution 1:
510, 510, 510
Verification:
(510 + 510 + 510) / 3 = 1530 / 3 ≈ 510
This solution is correct!
Solution 2:
510, 510, 510
Verification:
(510 + 510 + 510) / 3 = 1530 / 3 ≈ 510
This solution is correct!
Solution 3:
530, 549, 451
Verification:
(530 + 549 + 451) / 3 = 1530 / 3 ≈ 510
This solution is correct!
Solution 4:
1434, 60, 36
Verification:
(1434 + 60 + 36) / 3 = 1530 / 3 ≈ 510
This solution is correct!
Solution 5:
1400, 105, 25
Verification:
(1400 + 105 + 25) / 3 = 1530 / 3 ≈ 510
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 1530 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.