What three numbers have an average of 963?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 963. This means if we add these three numbers together and divide by 3, we should get 963.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 963 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 963 * 3 = x + y + z
- So, the sum of our three numbers should be: 2889
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2889.
Solution 1:
963, 963, 963
Verification:
(963 + 963 + 963) / 3 = 2889 / 3 ≈ 963
This solution is correct!
Solution 2:
963, 963, 963
Verification:
(963 + 963 + 963) / 3 = 2889 / 3 ≈ 963
This solution is correct!
Solution 3:
2209, 60, 620
Verification:
(2209 + 60 + 620) / 3 = 2889 / 3 ≈ 963
This solution is correct!
Solution 4:
2157, 675, 57
Verification:
(2157 + 675 + 57) / 3 = 2889 / 3 ≈ 963
This solution is correct!
Solution 5:
839, 1543, 507
Verification:
(839 + 1543 + 507) / 3 = 2889 / 3 ≈ 963
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 2889 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.