What three numbers have an average of 457?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 457. This means if we add these three numbers together and divide by 3, we should get 457.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 457 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 457 * 3 = x + y + z
- So, the sum of our three numbers should be: 1371
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1371.
Solution 1:
457, 457, 457
Verification:
(457 + 457 + 457) / 3 = 1371 / 3 ≈ 457
This solution is correct!
Solution 2:
457, 457, 457
Verification:
(457 + 457 + 457) / 3 = 1371 / 3 ≈ 457
This solution is correct!
Solution 3:
367, 907, 97
Verification:
(367 + 907 + 97) / 3 = 1371 / 3 ≈ 457
This solution is correct!
Solution 4:
1071, 52, 248
Verification:
(1071 + 52 + 248) / 3 = 1371 / 3 ≈ 457
This solution is correct!
Solution 5:
676, 665, 30
Verification:
(676 + 665 + 30) / 3 = 1371 / 3 ≈ 457
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 1371 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.