What three numbers have an average of 446?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 446. This means if we add these three numbers together and divide by 3, we should get 446.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 446 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 446 * 3 = x + y + z
- So, the sum of our three numbers should be: 1338
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1338.
Solution 1:
446, 446, 446
Verification:
(446 + 446 + 446) / 3 = 1338 / 3 ≈ 446
This solution is correct!
Solution 2:
446, 446, 446
Verification:
(446 + 446 + 446) / 3 = 1338 / 3 ≈ 446
This solution is correct!
Solution 3:
1268, 3, 67
Verification:
(1268 + 3 + 67) / 3 = 1338 / 3 ≈ 446
This solution is correct!
Solution 4:
114, 1206, 18
Verification:
(114 + 1206 + 18) / 3 = 1338 / 3 ≈ 446
This solution is correct!
Solution 5:
888, 7, 443
Verification:
(888 + 7 + 443) / 3 = 1338 / 3 ≈ 446
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 1338 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.