What three numbers have an average of 779?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 779. This means if we add these three numbers together and divide by 3, we should get 779.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 779 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 779 * 3 = x + y + z
- So, the sum of our three numbers should be: 2337
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2337.
Solution 1:
779, 779, 779
Verification:
(779 + 779 + 779) / 3 = 2337 / 3 ≈ 779
This solution is correct!
Solution 2:
779, 779, 779
Verification:
(779 + 779 + 779) / 3 = 2337 / 3 ≈ 779
This solution is correct!
Solution 3:
1418, 584, 335
Verification:
(1418 + 584 + 335) / 3 = 2337 / 3 ≈ 779
This solution is correct!
Solution 4:
822, 463, 1052
Verification:
(822 + 463 + 1052) / 3 = 2337 / 3 ≈ 779
This solution is correct!
Solution 5:
1117, 114, 1106
Verification:
(1117 + 114 + 1106) / 3 = 2337 / 3 ≈ 779
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 2337 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.