What three numbers have an average of 427?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 427. This means if we add these three numbers together and divide by 3, we should get 427.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 427 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 427 * 3 = x + y + z
- So, the sum of our three numbers should be: 1281
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1281.
Solution 1:
427, 427, 427
Verification:
(427 + 427 + 427) / 3 = 1281 / 3 ≈ 427
This solution is correct!
Solution 2:
427, 427, 427
Verification:
(427 + 427 + 427) / 3 = 1281 / 3 ≈ 427
This solution is correct!
Solution 3:
1129, 139, 13
Verification:
(1129 + 139 + 13) / 3 = 1281 / 3 ≈ 427
This solution is correct!
Solution 4:
991, 260, 30
Verification:
(991 + 260 + 30) / 3 = 1281 / 3 ≈ 427
This solution is correct!
Solution 5:
1156, 57, 68
Verification:
(1156 + 57 + 68) / 3 = 1281 / 3 ≈ 427
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 1281 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.