What three numbers have an average of 357?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 357. This means if we add these three numbers together and divide by 3, we should get 357.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 357 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 357 * 3 = x + y + z
- So, the sum of our three numbers should be: 1071
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1071.
Solution 1:
357, 357, 357
Verification:
(357 + 357 + 357) / 3 = 1071 / 3 ≈ 357
This solution is correct!
Solution 2:
357, 357, 357
Verification:
(357 + 357 + 357) / 3 = 1071 / 3 ≈ 357
This solution is correct!
Solution 3:
635, 343, 93
Verification:
(635 + 343 + 93) / 3 = 1071 / 3 ≈ 357
This solution is correct!
Solution 4:
926, 125, 20
Verification:
(926 + 125 + 20) / 3 = 1071 / 3 ≈ 357
This solution is correct!
Solution 5:
696, 198, 177
Verification:
(696 + 198 + 177) / 3 = 1071 / 3 ≈ 357
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 1071 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.