What three numbers have an average of 627?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 627. This means if we add these three numbers together and divide by 3, we should get 627.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 627 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 627 * 3 = x + y + z
- So, the sum of our three numbers should be: 1881
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1881.
Solution 1:
627, 627, 627
Verification:
(627 + 627 + 627) / 3 = 1881 / 3 ≈ 627
This solution is correct!
Solution 2:
627, 627, 627
Verification:
(627 + 627 + 627) / 3 = 1881 / 3 ≈ 627
This solution is correct!
Solution 3:
1108, 407, 366
Verification:
(1108 + 407 + 366) / 3 = 1881 / 3 ≈ 627
This solution is correct!
Solution 4:
9, 102, 1770
Verification:
(9 + 102 + 1770) / 3 = 1881 / 3 ≈ 627
This solution is correct!
Solution 5:
1063, 4, 814
Verification:
(1063 + 4 + 814) / 3 = 1881 / 3 ≈ 627
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 1881 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.