What three numbers have an average of 775?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 775. This means if we add these three numbers together and divide by 3, we should get 775.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 775 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 775 * 3 = x + y + z
- So, the sum of our three numbers should be: 2325
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2325.
Solution 1:
775, 775, 775
Verification:
(775 + 775 + 775) / 3 = 2325 / 3 ≈ 775
This solution is correct!
Solution 2:
775, 775, 775
Verification:
(775 + 775 + 775) / 3 = 2325 / 3 ≈ 775
This solution is correct!
Solution 3:
200, 212, 1913
Verification:
(200 + 212 + 1913) / 3 = 2325 / 3 ≈ 775
This solution is correct!
Solution 4:
2011, 283, 31
Verification:
(2011 + 283 + 31) / 3 = 2325 / 3 ≈ 775
This solution is correct!
Solution 5:
271, 544, 1510
Verification:
(271 + 544 + 1510) / 3 = 2325 / 3 ≈ 775
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 2325 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.