What three numbers have an average of 681?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 681. This means if we add these three numbers together and divide by 3, we should get 681.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 681 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 681 * 3 = x + y + z
- So, the sum of our three numbers should be: 2043
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2043.
Solution 1:
681, 681, 681
Verification:
(681 + 681 + 681) / 3 = 2043 / 3 ≈ 681
This solution is correct!
Solution 2:
681, 681, 681
Verification:
(681 + 681 + 681) / 3 = 2043 / 3 ≈ 681
This solution is correct!
Solution 3:
884, 566, 593
Verification:
(884 + 566 + 593) / 3 = 2043 / 3 ≈ 681
This solution is correct!
Solution 4:
650, 646, 747
Verification:
(650 + 646 + 747) / 3 = 2043 / 3 ≈ 681
This solution is correct!
Solution 5:
32, 1031, 980
Verification:
(32 + 1031 + 980) / 3 = 2043 / 3 ≈ 681
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 2043 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.