What three numbers have an average of 380?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 380. This means if we add these three numbers together and divide by 3, we should get 380.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 380 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 380 * 3 = x + y + z
- So, the sum of our three numbers should be: 1140
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1140.
Solution 1:
380, 380, 380
Verification:
(380 + 380 + 380) / 3 = 1140 / 3 ≈ 380
This solution is correct!
Solution 2:
380, 380, 380
Verification:
(380 + 380 + 380) / 3 = 1140 / 3 ≈ 380
This solution is correct!
Solution 3:
482, 82, 576
Verification:
(482 + 82 + 576) / 3 = 1140 / 3 ≈ 380
This solution is correct!
Solution 4:
829, 8, 303
Verification:
(829 + 8 + 303) / 3 = 1140 / 3 ≈ 380
This solution is correct!
Solution 5:
76, 930, 134
Verification:
(76 + 930 + 134) / 3 = 1140 / 3 ≈ 380
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 1140 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.