What three numbers have an average of 786?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 786. This means if we add these three numbers together and divide by 3, we should get 786.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 786 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 786 * 3 = x + y + z
- So, the sum of our three numbers should be: 2358
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2358.
Solution 1:
786, 786, 786
Verification:
(786 + 786 + 786) / 3 = 2358 / 3 ≈ 786
This solution is correct!
Solution 2:
786, 786, 786
Verification:
(786 + 786 + 786) / 3 = 2358 / 3 ≈ 786
This solution is correct!
Solution 3:
2272, 41, 45
Verification:
(2272 + 41 + 45) / 3 = 2358 / 3 ≈ 786
This solution is correct!
Solution 4:
196, 1960, 202
Verification:
(196 + 1960 + 202) / 3 = 2358 / 3 ≈ 786
This solution is correct!
Solution 5:
605, 928, 825
Verification:
(605 + 928 + 825) / 3 = 2358 / 3 ≈ 786
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 2358 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.