What three numbers have an average of 338?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 338. This means if we add these three numbers together and divide by 3, we should get 338.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 338 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 338 * 3 = x + y + z
- So, the sum of our three numbers should be: 1014
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1014.
Solution 1:
338, 338, 338
Verification:
(338 + 338 + 338) / 3 = 1014 / 3 ≈ 338
This solution is correct!
Solution 2:
338, 338, 338
Verification:
(338 + 338 + 338) / 3 = 1014 / 3 ≈ 338
This solution is correct!
Solution 3:
697, 316, 1
Verification:
(697 + 316 + 1) / 3 = 1014 / 3 ≈ 338
This solution is correct!
Solution 4:
234, 729, 51
Verification:
(234 + 729 + 51) / 3 = 1014 / 3 ≈ 338
This solution is correct!
Solution 5:
146, 142, 726
Verification:
(146 + 142 + 726) / 3 = 1014 / 3 ≈ 338
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 1014 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.