What three numbers have an average of 965?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 965. This means if we add these three numbers together and divide by 3, we should get 965.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 965 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 965 * 3 = x + y + z
- So, the sum of our three numbers should be: 2895
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2895.
Solution 1:
965, 965, 965
Verification:
(965 + 965 + 965) / 3 = 2895 / 3 ≈ 965
This solution is correct!
Solution 2:
965, 965, 965
Verification:
(965 + 965 + 965) / 3 = 2895 / 3 ≈ 965
This solution is correct!
Solution 3:
2407, 77, 411
Verification:
(2407 + 77 + 411) / 3 = 2895 / 3 ≈ 965
This solution is correct!
Solution 4:
645, 1807, 443
Verification:
(645 + 1807 + 443) / 3 = 2895 / 3 ≈ 965
This solution is correct!
Solution 5:
148, 2180, 567
Verification:
(148 + 2180 + 567) / 3 = 2895 / 3 ≈ 965
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 2895 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.