What three numbers have an average of 684?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 684. This means if we add these three numbers together and divide by 3, we should get 684.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 684 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 684 * 3 = x + y + z
- So, the sum of our three numbers should be: 2052
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2052.
Solution 1:
684, 684, 684
Verification:
(684 + 684 + 684) / 3 = 2052 / 3 ≈ 684
This solution is correct!
Solution 2:
684, 684, 684
Verification:
(684 + 684 + 684) / 3 = 2052 / 3 ≈ 684
This solution is correct!
Solution 3:
1510, 123, 419
Verification:
(1510 + 123 + 419) / 3 = 2052 / 3 ≈ 684
This solution is correct!
Solution 4:
1251, 308, 493
Verification:
(1251 + 308 + 493) / 3 = 2052 / 3 ≈ 684
This solution is correct!
Solution 5:
920, 382, 750
Verification:
(920 + 382 + 750) / 3 = 2052 / 3 ≈ 684
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 2052 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.