What three numbers have an average of 437?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 437. This means if we add these three numbers together and divide by 3, we should get 437.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 437 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 437 * 3 = x + y + z
- So, the sum of our three numbers should be: 1311
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1311.
Solution 1:
437, 437, 437
Verification:
(437 + 437 + 437) / 3 = 1311 / 3 ≈ 437
This solution is correct!
Solution 2:
437, 437, 437
Verification:
(437 + 437 + 437) / 3 = 1311 / 3 ≈ 437
This solution is correct!
Solution 3:
817, 238, 256
Verification:
(817 + 238 + 256) / 3 = 1311 / 3 ≈ 437
This solution is correct!
Solution 4:
662, 574, 75
Verification:
(662 + 574 + 75) / 3 = 1311 / 3 ≈ 437
This solution is correct!
Solution 5:
556, 317, 438
Verification:
(556 + 317 + 438) / 3 = 1311 / 3 ≈ 437
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 1311 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.