What three numbers have an average of 796?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 796. This means if we add these three numbers together and divide by 3, we should get 796.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 796 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 796 * 3 = x + y + z
- So, the sum of our three numbers should be: 2388
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2388.
Solution 1:
796, 796, 796
Verification:
(796 + 796 + 796) / 3 = 2388 / 3 ≈ 796
This solution is correct!
Solution 2:
796, 796, 796
Verification:
(796 + 796 + 796) / 3 = 2388 / 3 ≈ 796
This solution is correct!
Solution 3:
443, 123, 1822
Verification:
(443 + 123 + 1822) / 3 = 2388 / 3 ≈ 796
This solution is correct!
Solution 4:
1827, 221, 340
Verification:
(1827 + 221 + 340) / 3 = 2388 / 3 ≈ 796
This solution is correct!
Solution 5:
1570, 323, 495
Verification:
(1570 + 323 + 495) / 3 = 2388 / 3 ≈ 796
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 2388 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.