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:
198, 11, 931
Verification:
(198 + 11 + 931) / 3 = 1140 / 3 ≈ 380
This solution is correct!
Solution 4:
507, 580, 53
Verification:
(507 + 580 + 53) / 3 = 1140 / 3 ≈ 380
This solution is correct!
Solution 5:
666, 92, 382
Verification:
(666 + 92 + 382) / 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.