What three numbers have an average of 299?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 299. This means if we add these three numbers together and divide by 3, we should get 299.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 299 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 299 * 3 = x + y + z
- So, the sum of our three numbers should be: 897
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 897.
Solution 1:
299, 299, 299
Verification:
(299 + 299 + 299) / 3 = 897 / 3 ≈ 299
This solution is correct!
Solution 2:
299, 299, 299
Verification:
(299 + 299 + 299) / 3 = 897 / 3 ≈ 299
This solution is correct!
Solution 3:
765, 67, 65
Verification:
(765 + 67 + 65) / 3 = 897 / 3 ≈ 299
This solution is correct!
Solution 4:
285, 186, 426
Verification:
(285 + 186 + 426) / 3 = 897 / 3 ≈ 299
This solution is correct!
Solution 5:
469, 59, 369
Verification:
(469 + 59 + 369) / 3 = 897 / 3 ≈ 299
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 897 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.