What three numbers have an average of 999?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 999. This means if we add these three numbers together and divide by 3, we should get 999.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 999 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 999 * 3 = x + y + z
- So, the sum of our three numbers should be: 2997
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2997.
Solution 1:
999, 999, 999
Verification:
(999 + 999 + 999) / 3 = 2997 / 3 ≈ 999
This solution is correct!
Solution 2:
999, 999, 999
Verification:
(999 + 999 + 999) / 3 = 2997 / 3 ≈ 999
This solution is correct!
Solution 3:
905, 1869, 223
Verification:
(905 + 1869 + 223) / 3 = 2997 / 3 ≈ 999
This solution is correct!
Solution 4:
264, 1423, 1310
Verification:
(264 + 1423 + 1310) / 3 = 2997 / 3 ≈ 999
This solution is correct!
Solution 5:
2015, 156, 826
Verification:
(2015 + 156 + 826) / 3 = 2997 / 3 ≈ 999
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 2997 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.