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:
247, 422, 249
Verification:
(247 + 422 + 249) / 3 = 918 / 3 ≈ 306
This solution is correct!
Solution 4:
541, 122, 255
Verification:
(541 + 122 + 255) / 3 = 918 / 3 ≈ 306
This solution is correct!
Solution 5:
240, 254, 424
Verification:
(240 + 254 + 424) / 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.