What three numbers have an average of 646?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 646. This means if we add these three numbers together and divide by 3, we should get 646.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 646 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 646 * 3 = x + y + z
- So, the sum of our three numbers should be: 1938
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1938.
Solution 1:
646, 646, 646
Verification:
(646 + 646 + 646) / 3 = 1938 / 3 ≈ 646
This solution is correct!
Solution 2:
646, 646, 646
Verification:
(646 + 646 + 646) / 3 = 1938 / 3 ≈ 646
This solution is correct!
Solution 3:
237, 664, 1037
Verification:
(237 + 664 + 1037) / 3 = 1938 / 3 ≈ 646
This solution is correct!
Solution 4:
120, 920, 898
Verification:
(120 + 920 + 898) / 3 = 1938 / 3 ≈ 646
This solution is correct!
Solution 5:
1855, 31, 52
Verification:
(1855 + 31 + 52) / 3 = 1938 / 3 ≈ 646
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 1938 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.