What three numbers have an average of 384?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 384. This means if we add these three numbers together and divide by 3, we should get 384.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 384 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 384 * 3 = x + y + z
- So, the sum of our three numbers should be: 1152
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1152.
Solution 1:
384, 384, 384
Verification:
(384 + 384 + 384) / 3 = 1152 / 3 ≈ 384
This solution is correct!
Solution 2:
384, 384, 384
Verification:
(384 + 384 + 384) / 3 = 1152 / 3 ≈ 384
This solution is correct!
Solution 3:
561, 180, 411
Verification:
(561 + 180 + 411) / 3 = 1152 / 3 ≈ 384
This solution is correct!
Solution 4:
60, 176, 916
Verification:
(60 + 176 + 916) / 3 = 1152 / 3 ≈ 384
This solution is correct!
Solution 5:
51, 550, 551
Verification:
(51 + 550 + 551) / 3 = 1152 / 3 ≈ 384
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 1152 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.