What three numbers have an average of 385?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 385. This means if we add these three numbers together and divide by 3, we should get 385.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 385 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 385 * 3 = x + y + z
- So, the sum of our three numbers should be: 1155
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1155.
Solution 1:
385, 385, 385
Verification:
(385 + 385 + 385) / 3 = 1155 / 3 ≈ 385
This solution is correct!
Solution 2:
385, 385, 385
Verification:
(385 + 385 + 385) / 3 = 1155 / 3 ≈ 385
This solution is correct!
Solution 3:
299, 212, 644
Verification:
(299 + 212 + 644) / 3 = 1155 / 3 ≈ 385
This solution is correct!
Solution 4:
460, 400, 295
Verification:
(460 + 400 + 295) / 3 = 1155 / 3 ≈ 385
This solution is correct!
Solution 5:
362, 618, 175
Verification:
(362 + 618 + 175) / 3 = 1155 / 3 ≈ 385
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 1155 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.