What three numbers have an average of 395?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 395. This means if we add these three numbers together and divide by 3, we should get 395.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 395 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 395 * 3 = x + y + z
- So, the sum of our three numbers should be: 1185
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1185.
Solution 1:
395, 395, 395
Verification:
(395 + 395 + 395) / 3 = 1185 / 3 ≈ 395
This solution is correct!
Solution 2:
395, 395, 395
Verification:
(395 + 395 + 395) / 3 = 1185 / 3 ≈ 395
This solution is correct!
Solution 3:
6, 884, 295
Verification:
(6 + 884 + 295) / 3 = 1185 / 3 ≈ 395
This solution is correct!
Solution 4:
451, 506, 228
Verification:
(451 + 506 + 228) / 3 = 1185 / 3 ≈ 395
This solution is correct!
Solution 5:
135, 1031, 19
Verification:
(135 + 1031 + 19) / 3 = 1185 / 3 ≈ 395
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 1185 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.