What three numbers have an average of 964?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 964. This means if we add these three numbers together and divide by 3, we should get 964.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 964 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 964 * 3 = x + y + z
- So, the sum of our three numbers should be: 2892
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2892.
Solution 1:
964, 964, 964
Verification:
(964 + 964 + 964) / 3 = 2892 / 3 ≈ 964
This solution is correct!
Solution 2:
964, 964, 964
Verification:
(964 + 964 + 964) / 3 = 2892 / 3 ≈ 964
This solution is correct!
Solution 3:
753, 715, 1424
Verification:
(753 + 715 + 1424) / 3 = 2892 / 3 ≈ 964
This solution is correct!
Solution 4:
384, 1781, 727
Verification:
(384 + 1781 + 727) / 3 = 2892 / 3 ≈ 964
This solution is correct!
Solution 5:
845, 304, 1743
Verification:
(845 + 304 + 1743) / 3 = 2892 / 3 ≈ 964
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 2892 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.