What three numbers have an average of 680?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 680. This means if we add these three numbers together and divide by 3, we should get 680.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 680 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 680 * 3 = x + y + z
- So, the sum of our three numbers should be: 2040
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2040.
Solution 1:
680, 680, 680
Verification:
(680 + 680 + 680) / 3 = 2040 / 3 ≈ 680
This solution is correct!
Solution 2:
680, 680, 680
Verification:
(680 + 680 + 680) / 3 = 2040 / 3 ≈ 680
This solution is correct!
Solution 3:
1252, 407, 381
Verification:
(1252 + 407 + 381) / 3 = 2040 / 3 ≈ 680
This solution is correct!
Solution 4:
1243, 640, 157
Verification:
(1243 + 640 + 157) / 3 = 2040 / 3 ≈ 680
This solution is correct!
Solution 5:
286, 827, 927
Verification:
(286 + 827 + 927) / 3 = 2040 / 3 ≈ 680
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 2040 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.