What three numbers have an average of 448?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 448. This means if we add these three numbers together and divide by 3, we should get 448.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 448 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 448 * 3 = x + y + z
- So, the sum of our three numbers should be: 1344
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1344.
Solution 1:
448, 448, 448
Verification:
(448 + 448 + 448) / 3 = 1344 / 3 ≈ 448
This solution is correct!
Solution 2:
448, 448, 448
Verification:
(448 + 448 + 448) / 3 = 1344 / 3 ≈ 448
This solution is correct!
Solution 3:
817, 485, 42
Verification:
(817 + 485 + 42) / 3 = 1344 / 3 ≈ 448
This solution is correct!
Solution 4:
275, 421, 648
Verification:
(275 + 421 + 648) / 3 = 1344 / 3 ≈ 448
This solution is correct!
Solution 5:
29, 1131, 184
Verification:
(29 + 1131 + 184) / 3 = 1344 / 3 ≈ 448
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 1344 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.