What three numbers have an average of 382?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 382. This means if we add these three numbers together and divide by 3, we should get 382.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 382 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 382 * 3 = x + y + z
- So, the sum of our three numbers should be: 1146
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1146.
Solution 1:
382, 382, 382
Verification:
(382 + 382 + 382) / 3 = 1146 / 3 ≈ 382
This solution is correct!
Solution 2:
382, 382, 382
Verification:
(382 + 382 + 382) / 3 = 1146 / 3 ≈ 382
This solution is correct!
Solution 3:
814, 118, 214
Verification:
(814 + 118 + 214) / 3 = 1146 / 3 ≈ 382
This solution is correct!
Solution 4:
488, 108, 550
Verification:
(488 + 108 + 550) / 3 = 1146 / 3 ≈ 382
This solution is correct!
Solution 5:
774, 233, 139
Verification:
(774 + 233 + 139) / 3 = 1146 / 3 ≈ 382
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 1146 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.