What three numbers have an average of 379?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 379. This means if we add these three numbers together and divide by 3, we should get 379.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 379 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 379 * 3 = x + y + z
- So, the sum of our three numbers should be: 1137
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1137.
Solution 1:
379, 379, 379
Verification:
(379 + 379 + 379) / 3 = 1137 / 3 ≈ 379
This solution is correct!
Solution 2:
379, 379, 379
Verification:
(379 + 379 + 379) / 3 = 1137 / 3 ≈ 379
This solution is correct!
Solution 3:
198, 825, 114
Verification:
(198 + 825 + 114) / 3 = 1137 / 3 ≈ 379
This solution is correct!
Solution 4:
708, 420, 9
Verification:
(708 + 420 + 9) / 3 = 1137 / 3 ≈ 379
This solution is correct!
Solution 5:
892, 140, 105
Verification:
(892 + 140 + 105) / 3 = 1137 / 3 ≈ 379
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 1137 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.