What three numbers have an average of 306?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 306. This means if we add these three numbers together and divide by 3, we should get 306.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 306 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 306 * 3 = x + y + z
- So, the sum of our three numbers should be: 918
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 918.
Solution 1:
306, 306, 306
Verification:
(306 + 306 + 306) / 3 = 918 / 3 ≈ 306
This solution is correct!
Solution 2:
306, 306, 306
Verification:
(306 + 306 + 306) / 3 = 918 / 3 ≈ 306
This solution is correct!
Solution 3:
11, 43, 864
Verification:
(11 + 43 + 864) / 3 = 918 / 3 ≈ 306
This solution is correct!
Solution 4:
188, 360, 370
Verification:
(188 + 360 + 370) / 3 = 918 / 3 ≈ 306
This solution is correct!
Solution 5:
417, 68, 433
Verification:
(417 + 68 + 433) / 3 = 918 / 3 ≈ 306
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 918 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.