What three numbers have an average of 305?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 305. This means if we add these three numbers together and divide by 3, we should get 305.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 305 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 305 * 3 = x + y + z
- So, the sum of our three numbers should be: 915
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 915.
Solution 1:
305, 305, 305
Verification:
(305 + 305 + 305) / 3 = 915 / 3 ≈ 305
This solution is correct!
Solution 2:
305, 305, 305
Verification:
(305 + 305 + 305) / 3 = 915 / 3 ≈ 305
This solution is correct!
Solution 3:
910, 1, 4
Verification:
(910 + 1 + 4) / 3 = 915 / 3 ≈ 305
This solution is correct!
Solution 4:
605, 34, 276
Verification:
(605 + 34 + 276) / 3 = 915 / 3 ≈ 305
This solution is correct!
Solution 5:
389, 509, 17
Verification:
(389 + 509 + 17) / 3 = 915 / 3 ≈ 305
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 915 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.