What three numbers have an average of 863?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 863. This means if we add these three numbers together and divide by 3, we should get 863.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 863 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 863 * 3 = x + y + z
- So, the sum of our three numbers should be: 2589
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2589.
Solution 1:
863, 863, 863
Verification:
(863 + 863 + 863) / 3 = 2589 / 3 ≈ 863
This solution is correct!
Solution 2:
863, 863, 863
Verification:
(863 + 863 + 863) / 3 = 2589 / 3 ≈ 863
This solution is correct!
Solution 3:
1144, 1088, 357
Verification:
(1144 + 1088 + 357) / 3 = 2589 / 3 ≈ 863
This solution is correct!
Solution 4:
103, 1916, 570
Verification:
(103 + 1916 + 570) / 3 = 2589 / 3 ≈ 863
This solution is correct!
Solution 5:
261, 829, 1499
Verification:
(261 + 829 + 1499) / 3 = 2589 / 3 ≈ 863
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 2589 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.