What three numbers have an average of 638?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 638. This means if we add these three numbers together and divide by 3, we should get 638.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 638 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 638 * 3 = x + y + z
- So, the sum of our three numbers should be: 1914
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1914.
Solution 1:
638, 638, 638
Verification:
(638 + 638 + 638) / 3 = 1914 / 3 ≈ 638
This solution is correct!
Solution 2:
638, 638, 638
Verification:
(638 + 638 + 638) / 3 = 1914 / 3 ≈ 638
This solution is correct!
Solution 3:
174, 1112, 628
Verification:
(174 + 1112 + 628) / 3 = 1914 / 3 ≈ 638
This solution is correct!
Solution 4:
1069, 205, 640
Verification:
(1069 + 205 + 640) / 3 = 1914 / 3 ≈ 638
This solution is correct!
Solution 5:
694, 175, 1045
Verification:
(694 + 175 + 1045) / 3 = 1914 / 3 ≈ 638
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 1914 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.