What three numbers have an average of 455?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 455. This means if we add these three numbers together and divide by 3, we should get 455.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 455 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 455 * 3 = x + y + z
- So, the sum of our three numbers should be: 1365
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1365.
Solution 1:
455, 455, 455
Verification:
(455 + 455 + 455) / 3 = 1365 / 3 ≈ 455
This solution is correct!
Solution 2:
455, 455, 455
Verification:
(455 + 455 + 455) / 3 = 1365 / 3 ≈ 455
This solution is correct!
Solution 3:
267, 164, 934
Verification:
(267 + 164 + 934) / 3 = 1365 / 3 ≈ 455
This solution is correct!
Solution 4:
946, 347, 72
Verification:
(946 + 347 + 72) / 3 = 1365 / 3 ≈ 455
This solution is correct!
Solution 5:
120, 1175, 70
Verification:
(120 + 1175 + 70) / 3 = 1365 / 3 ≈ 455
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 1365 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.