What three numbers have an average of 806?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 806. This means if we add these three numbers together and divide by 3, we should get 806.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 806 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 806 * 3 = x + y + z
- So, the sum of our three numbers should be: 2418
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2418.
Solution 1:
806, 806, 806
Verification:
(806 + 806 + 806) / 3 = 2418 / 3 ≈ 806
This solution is correct!
Solution 2:
806, 806, 806
Verification:
(806 + 806 + 806) / 3 = 2418 / 3 ≈ 806
This solution is correct!
Solution 3:
595, 1751, 72
Verification:
(595 + 1751 + 72) / 3 = 2418 / 3 ≈ 806
This solution is correct!
Solution 4:
426, 1652, 340
Verification:
(426 + 1652 + 340) / 3 = 2418 / 3 ≈ 806
This solution is correct!
Solution 5:
366, 1037, 1015
Verification:
(366 + 1037 + 1015) / 3 = 2418 / 3 ≈ 806
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 2418 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.