What three numbers have an average of 417?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 417. This means if we add these three numbers together and divide by 3, we should get 417.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 417 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 417 * 3 = x + y + z
- So, the sum of our three numbers should be: 1251
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1251.
Solution 1:
417, 417, 417
Verification:
(417 + 417 + 417) / 3 = 1251 / 3 ≈ 417
This solution is correct!
Solution 2:
417, 417, 417
Verification:
(417 + 417 + 417) / 3 = 1251 / 3 ≈ 417
This solution is correct!
Solution 3:
1234, 3, 14
Verification:
(1234 + 3 + 14) / 3 = 1251 / 3 ≈ 417
This solution is correct!
Solution 4:
1197, 42, 12
Verification:
(1197 + 42 + 12) / 3 = 1251 / 3 ≈ 417
This solution is correct!
Solution 5:
164, 643, 444
Verification:
(164 + 643 + 444) / 3 = 1251 / 3 ≈ 417
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 1251 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.