What three numbers have an average of 765?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 765. This means if we add these three numbers together and divide by 3, we should get 765.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 765 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 765 * 3 = x + y + z
- So, the sum of our three numbers should be: 2295
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2295.
Solution 1:
765, 765, 765
Verification:
(765 + 765 + 765) / 3 = 2295 / 3 ≈ 765
This solution is correct!
Solution 2:
765, 765, 765
Verification:
(765 + 765 + 765) / 3 = 2295 / 3 ≈ 765
This solution is correct!
Solution 3:
1021, 911, 363
Verification:
(1021 + 911 + 363) / 3 = 2295 / 3 ≈ 765
This solution is correct!
Solution 4:
1061, 1158, 76
Verification:
(1061 + 1158 + 76) / 3 = 2295 / 3 ≈ 765
This solution is correct!
Solution 5:
1764, 184, 347
Verification:
(1764 + 184 + 347) / 3 = 2295 / 3 ≈ 765
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 2295 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.