What three numbers have an average of 945?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 945. This means if we add these three numbers together and divide by 3, we should get 945.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 945 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 945 * 3 = x + y + z
- So, the sum of our three numbers should be: 2835
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2835.
Solution 1:
945, 945, 945
Verification:
(945 + 945 + 945) / 3 = 2835 / 3 ≈ 945
This solution is correct!
Solution 2:
945, 945, 945
Verification:
(945 + 945 + 945) / 3 = 2835 / 3 ≈ 945
This solution is correct!
Solution 3:
2622, 52, 161
Verification:
(2622 + 52 + 161) / 3 = 2835 / 3 ≈ 945
This solution is correct!
Solution 4:
2434, 143, 258
Verification:
(2434 + 143 + 258) / 3 = 2835 / 3 ≈ 945
This solution is correct!
Solution 5:
49, 2229, 557
Verification:
(49 + 2229 + 557) / 3 = 2835 / 3 ≈ 945
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 2835 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.