What three numbers have an average of 353?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 353. This means if we add these three numbers together and divide by 3, we should get 353.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 353 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 353 * 3 = x + y + z
- So, the sum of our three numbers should be: 1059
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1059.
Solution 1:
353, 353, 353
Verification:
(353 + 353 + 353) / 3 = 1059 / 3 ≈ 353
This solution is correct!
Solution 2:
353, 353, 353
Verification:
(353 + 353 + 353) / 3 = 1059 / 3 ≈ 353
This solution is correct!
Solution 3:
446, 284, 329
Verification:
(446 + 284 + 329) / 3 = 1059 / 3 ≈ 353
This solution is correct!
Solution 4:
207, 105, 747
Verification:
(207 + 105 + 747) / 3 = 1059 / 3 ≈ 353
This solution is correct!
Solution 5:
810, 222, 27
Verification:
(810 + 222 + 27) / 3 = 1059 / 3 ≈ 353
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 1059 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.