What three numbers have an average of 683?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 683. This means if we add these three numbers together and divide by 3, we should get 683.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 683 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 683 * 3 = x + y + z
- So, the sum of our three numbers should be: 2049
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2049.
Solution 1:
683, 683, 683
Verification:
(683 + 683 + 683) / 3 = 2049 / 3 ≈ 683
This solution is correct!
Solution 2:
683, 683, 683
Verification:
(683 + 683 + 683) / 3 = 2049 / 3 ≈ 683
This solution is correct!
Solution 3:
1604, 292, 153
Verification:
(1604 + 292 + 153) / 3 = 2049 / 3 ≈ 683
This solution is correct!
Solution 4:
621, 341, 1087
Verification:
(621 + 341 + 1087) / 3 = 2049 / 3 ≈ 683
This solution is correct!
Solution 5:
164, 1308, 577
Verification:
(164 + 1308 + 577) / 3 = 2049 / 3 ≈ 683
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 2049 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.