What three numbers have an average of 438?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 438. This means if we add these three numbers together and divide by 3, we should get 438.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 438 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 438 * 3 = x + y + z
- So, the sum of our three numbers should be: 1314
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1314.
Solution 1:
438, 438, 438
Verification:
(438 + 438 + 438) / 3 = 1314 / 3 ≈ 438
This solution is correct!
Solution 2:
438, 438, 438
Verification:
(438 + 438 + 438) / 3 = 1314 / 3 ≈ 438
This solution is correct!
Solution 3:
395, 512, 407
Verification:
(395 + 512 + 407) / 3 = 1314 / 3 ≈ 438
This solution is correct!
Solution 4:
719, 89, 506
Verification:
(719 + 89 + 506) / 3 = 1314 / 3 ≈ 438
This solution is correct!
Solution 5:
416, 769, 129
Verification:
(416 + 769 + 129) / 3 = 1314 / 3 ≈ 438
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 1314 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.