What three numbers have an average of 805?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 805. This means if we add these three numbers together and divide by 3, we should get 805.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 805 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 805 * 3 = x + y + z
- So, the sum of our three numbers should be: 2415
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2415.
Solution 1:
805, 805, 805
Verification:
(805 + 805 + 805) / 3 = 2415 / 3 ≈ 805
This solution is correct!
Solution 2:
805, 805, 805
Verification:
(805 + 805 + 805) / 3 = 2415 / 3 ≈ 805
This solution is correct!
Solution 3:
473, 984, 958
Verification:
(473 + 984 + 958) / 3 = 2415 / 3 ≈ 805
This solution is correct!
Solution 4:
2368, 23, 24
Verification:
(2368 + 23 + 24) / 3 = 2415 / 3 ≈ 805
This solution is correct!
Solution 5:
554, 117, 1744
Verification:
(554 + 117 + 1744) / 3 = 2415 / 3 ≈ 805
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 2415 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.