What three numbers have an average of 605?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 605. This means if we add these three numbers together and divide by 3, we should get 605.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 605 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 605 * 3 = x + y + z
- So, the sum of our three numbers should be: 1815
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1815.
Solution 1:
605, 605, 605
Verification:
(605 + 605 + 605) / 3 = 1815 / 3 ≈ 605
This solution is correct!
Solution 2:
605, 605, 605
Verification:
(605 + 605 + 605) / 3 = 1815 / 3 ≈ 605
This solution is correct!
Solution 3:
1445, 235, 135
Verification:
(1445 + 235 + 135) / 3 = 1815 / 3 ≈ 605
This solution is correct!
Solution 4:
1806, 4, 5
Verification:
(1806 + 4 + 5) / 3 = 1815 / 3 ≈ 605
This solution is correct!
Solution 5:
1017, 481, 317
Verification:
(1017 + 481 + 317) / 3 = 1815 / 3 ≈ 605
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 1815 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.