What three numbers have an average of 428?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 428. This means if we add these three numbers together and divide by 3, we should get 428.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 428 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 428 * 3 = x + y + z
- So, the sum of our three numbers should be: 1284
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1284.
Solution 1:
428, 428, 428
Verification:
(428 + 428 + 428) / 3 = 1284 / 3 ≈ 428
This solution is correct!
Solution 2:
428, 428, 428
Verification:
(428 + 428 + 428) / 3 = 1284 / 3 ≈ 428
This solution is correct!
Solution 3:
1045, 170, 69
Verification:
(1045 + 170 + 69) / 3 = 1284 / 3 ≈ 428
This solution is correct!
Solution 4:
11, 866, 407
Verification:
(11 + 866 + 407) / 3 = 1284 / 3 ≈ 428
This solution is correct!
Solution 5:
1212, 23, 49
Verification:
(1212 + 23 + 49) / 3 = 1284 / 3 ≈ 428
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 1284 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.