What three numbers have an average of 990?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 990. This means if we add these three numbers together and divide by 3, we should get 990.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 990 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 990 * 3 = x + y + z
- So, the sum of our three numbers should be: 2970
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2970.
Solution 1:
990, 990, 990
Verification:
(990 + 990 + 990) / 3 = 2970 / 3 ≈ 990
This solution is correct!
Solution 2:
990, 990, 990
Verification:
(990 + 990 + 990) / 3 = 2970 / 3 ≈ 990
This solution is correct!
Solution 3:
1914, 270, 786
Verification:
(1914 + 270 + 786) / 3 = 2970 / 3 ≈ 990
This solution is correct!
Solution 4:
2158, 553, 259
Verification:
(2158 + 553 + 259) / 3 = 2970 / 3 ≈ 990
This solution is correct!
Solution 5:
990, 1012, 968
Verification:
(990 + 1012 + 968) / 3 = 2970 / 3 ≈ 990
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 2970 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.