What three numbers have an average of 685?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 685. This means if we add these three numbers together and divide by 3, we should get 685.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 685 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 685 * 3 = x + y + z
- So, the sum of our three numbers should be: 2055
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2055.
Solution 1:
685, 685, 685
Verification:
(685 + 685 + 685) / 3 = 2055 / 3 ≈ 685
This solution is correct!
Solution 2:
685, 685, 685
Verification:
(685 + 685 + 685) / 3 = 2055 / 3 ≈ 685
This solution is correct!
Solution 3:
1894, 70, 91
Verification:
(1894 + 70 + 91) / 3 = 2055 / 3 ≈ 685
This solution is correct!
Solution 4:
1094, 811, 150
Verification:
(1094 + 811 + 150) / 3 = 2055 / 3 ≈ 685
This solution is correct!
Solution 5:
201, 459, 1395
Verification:
(201 + 459 + 1395) / 3 = 2055 / 3 ≈ 685
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 2055 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.