What three numbers have an average of 300?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 300. This means if we add these three numbers together and divide by 3, we should get 300.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 300 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 300 * 3 = x + y + z
- So, the sum of our three numbers should be: 900
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 900.
Solution 1:
300, 300, 300
Verification:
(300 + 300 + 300) / 3 = 900 / 3 ≈ 300
This solution is correct!
Solution 2:
300, 300, 300
Verification:
(300 + 300 + 300) / 3 = 900 / 3 ≈ 300
This solution is correct!
Solution 3:
471, 42, 387
Verification:
(471 + 42 + 387) / 3 = 900 / 3 ≈ 300
This solution is correct!
Solution 4:
440, 46, 414
Verification:
(440 + 46 + 414) / 3 = 900 / 3 ≈ 300
This solution is correct!
Solution 5:
60, 90, 750
Verification:
(60 + 90 + 750) / 3 = 900 / 3 ≈ 300
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 900 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.