What three numbers have an average of 864?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 864. This means if we add these three numbers together and divide by 3, we should get 864.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 864 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 864 * 3 = x + y + z
- So, the sum of our three numbers should be: 2592
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2592.
Solution 1:
864, 864, 864
Verification:
(864 + 864 + 864) / 3 = 2592 / 3 ≈ 864
This solution is correct!
Solution 2:
864, 864, 864
Verification:
(864 + 864 + 864) / 3 = 2592 / 3 ≈ 864
This solution is correct!
Solution 3:
1302, 1049, 241
Verification:
(1302 + 1049 + 241) / 3 = 2592 / 3 ≈ 864
This solution is correct!
Solution 4:
1097, 342, 1153
Verification:
(1097 + 342 + 1153) / 3 = 2592 / 3 ≈ 864
This solution is correct!
Solution 5:
2134, 400, 58
Verification:
(2134 + 400 + 58) / 3 = 2592 / 3 ≈ 864
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 2592 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.