What three numbers have an average of 609?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 609. This means if we add these three numbers together and divide by 3, we should get 609.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 609 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 609 * 3 = x + y + z
- So, the sum of our three numbers should be: 1827
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1827.
Solution 1:
609, 609, 609
Verification:
(609 + 609 + 609) / 3 = 1827 / 3 ≈ 609
This solution is correct!
Solution 2:
609, 609, 609
Verification:
(609 + 609 + 609) / 3 = 1827 / 3 ≈ 609
This solution is correct!
Solution 3:
264, 403, 1160
Verification:
(264 + 403 + 1160) / 3 = 1827 / 3 ≈ 609
This solution is correct!
Solution 4:
1721, 67, 39
Verification:
(1721 + 67 + 39) / 3 = 1827 / 3 ≈ 609
This solution is correct!
Solution 5:
136, 850, 841
Verification:
(136 + 850 + 841) / 3 = 1827 / 3 ≈ 609
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 1827 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.