What three numbers have an average of 381?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 381. This means if we add these three numbers together and divide by 3, we should get 381.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 381 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 381 * 3 = x + y + z
- So, the sum of our three numbers should be: 1143
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1143.
Solution 1:
381, 381, 381
Verification:
(381 + 381 + 381) / 3 = 1143 / 3 ≈ 381
This solution is correct!
Solution 2:
381, 381, 381
Verification:
(381 + 381 + 381) / 3 = 1143 / 3 ≈ 381
This solution is correct!
Solution 3:
1043, 98, 2
Verification:
(1043 + 98 + 2) / 3 = 1143 / 3 ≈ 381
This solution is correct!
Solution 4:
922, 62, 159
Verification:
(922 + 62 + 159) / 3 = 1143 / 3 ≈ 381
This solution is correct!
Solution 5:
764, 147, 232
Verification:
(764 + 147 + 232) / 3 = 1143 / 3 ≈ 381
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 1143 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.