What three numbers have an average of 509?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 509. This means if we add these three numbers together and divide by 3, we should get 509.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 509 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 509 * 3 = x + y + z
- So, the sum of our three numbers should be: 1527
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1527.
Solution 1:
509, 509, 509
Verification:
(509 + 509 + 509) / 3 = 1527 / 3 ≈ 509
This solution is correct!
Solution 2:
509, 509, 509
Verification:
(509 + 509 + 509) / 3 = 1527 / 3 ≈ 509
This solution is correct!
Solution 3:
565, 236, 726
Verification:
(565 + 236 + 726) / 3 = 1527 / 3 ≈ 509
This solution is correct!
Solution 4:
280, 550, 697
Verification:
(280 + 550 + 697) / 3 = 1527 / 3 ≈ 509
This solution is correct!
Solution 5:
508, 358, 661
Verification:
(508 + 358 + 661) / 3 = 1527 / 3 ≈ 509
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 1527 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.