What three numbers have an average of 622?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 622. This means if we add these three numbers together and divide by 3, we should get 622.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 622 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 622 * 3 = x + y + z
- So, the sum of our three numbers should be: 1866
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1866.
Solution 1:
622, 622, 622
Verification:
(622 + 622 + 622) / 3 = 1866 / 3 ≈ 622
This solution is correct!
Solution 2:
622, 622, 622
Verification:
(622 + 622 + 622) / 3 = 1866 / 3 ≈ 622
This solution is correct!
Solution 3:
450, 59, 1357
Verification:
(450 + 59 + 1357) / 3 = 1866 / 3 ≈ 622
This solution is correct!
Solution 4:
137, 1565, 164
Verification:
(137 + 1565 + 164) / 3 = 1866 / 3 ≈ 622
This solution is correct!
Solution 5:
891, 521, 454
Verification:
(891 + 521 + 454) / 3 = 1866 / 3 ≈ 622
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 1866 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.