What three numbers have an average of 649?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 649. This means if we add these three numbers together and divide by 3, we should get 649.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 649 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 649 * 3 = x + y + z
- So, the sum of our three numbers should be: 1947
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1947.
Solution 1:
649, 649, 649
Verification:
(649 + 649 + 649) / 3 = 1947 / 3 ≈ 649
This solution is correct!
Solution 2:
649, 649, 649
Verification:
(649 + 649 + 649) / 3 = 1947 / 3 ≈ 649
This solution is correct!
Solution 3:
1264, 44, 639
Verification:
(1264 + 44 + 639) / 3 = 1947 / 3 ≈ 649
This solution is correct!
Solution 4:
1440, 242, 265
Verification:
(1440 + 242 + 265) / 3 = 1947 / 3 ≈ 649
This solution is correct!
Solution 5:
1216, 86, 645
Verification:
(1216 + 86 + 645) / 3 = 1947 / 3 ≈ 649
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 1947 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.