What three numbers have an average of 966?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 966. This means if we add these three numbers together and divide by 3, we should get 966.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 966 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 966 * 3 = x + y + z
- So, the sum of our three numbers should be: 2898
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2898.
Solution 1:
966, 966, 966
Verification:
(966 + 966 + 966) / 3 = 2898 / 3 ≈ 966
This solution is correct!
Solution 2:
966, 966, 966
Verification:
(966 + 966 + 966) / 3 = 2898 / 3 ≈ 966
This solution is correct!
Solution 3:
1891, 11, 996
Verification:
(1891 + 11 + 996) / 3 = 2898 / 3 ≈ 966
This solution is correct!
Solution 4:
1697, 353, 848
Verification:
(1697 + 353 + 848) / 3 = 2898 / 3 ≈ 966
This solution is correct!
Solution 5:
2478, 67, 353
Verification:
(2478 + 67 + 353) / 3 = 2898 / 3 ≈ 966
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 2898 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.