What three numbers have an average of 398?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 398. This means if we add these three numbers together and divide by 3, we should get 398.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 398 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 398 * 3 = x + y + z
- So, the sum of our three numbers should be: 1194
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1194.
Solution 1:
398, 398, 398
Verification:
(398 + 398 + 398) / 3 = 1194 / 3 ≈ 398
This solution is correct!
Solution 2:
398, 398, 398
Verification:
(398 + 398 + 398) / 3 = 1194 / 3 ≈ 398
This solution is correct!
Solution 3:
562, 540, 92
Verification:
(562 + 540 + 92) / 3 = 1194 / 3 ≈ 398
This solution is correct!
Solution 4:
491, 318, 385
Verification:
(491 + 318 + 385) / 3 = 1194 / 3 ≈ 398
This solution is correct!
Solution 5:
313, 119, 762
Verification:
(313 + 119 + 762) / 3 = 1194 / 3 ≈ 398
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 1194 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.