What three numbers have an average of 949?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 949. This means if we add these three numbers together and divide by 3, we should get 949.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 949 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 949 * 3 = x + y + z
- So, the sum of our three numbers should be: 2847
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2847.
Solution 1:
949, 949, 949
Verification:
(949 + 949 + 949) / 3 = 2847 / 3 ≈ 949
This solution is correct!
Solution 2:
949, 949, 949
Verification:
(949 + 949 + 949) / 3 = 2847 / 3 ≈ 949
This solution is correct!
Solution 3:
212, 2426, 209
Verification:
(212 + 2426 + 209) / 3 = 2847 / 3 ≈ 949
This solution is correct!
Solution 4:
2832, 2, 13
Verification:
(2832 + 2 + 13) / 3 = 2847 / 3 ≈ 949
This solution is correct!
Solution 5:
1986, 670, 191
Verification:
(1986 + 670 + 191) / 3 = 2847 / 3 ≈ 949
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 2847 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.