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:
21, 1561, 836
Verification:
(21 + 1561 + 836) / 3 = 2418 / 3 ≈ 806
This solution is correct!
Solution 4:
1412, 746, 260
Verification:
(1412 + 746 + 260) / 3 = 2418 / 3 ≈ 806
This solution is correct!
Solution 5:
813, 971, 634
Verification:
(813 + 971 + 634) / 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.