What three numbers have an average of 459?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 459. This means if we add these three numbers together and divide by 3, we should get 459.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 459 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 459 * 3 = x + y + z
- So, the sum of our three numbers should be: 1377
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1377.
Solution 1:
459, 459, 459
Verification:
(459 + 459 + 459) / 3 = 1377 / 3 ≈ 459
This solution is correct!
Solution 2:
459, 459, 459
Verification:
(459 + 459 + 459) / 3 = 1377 / 3 ≈ 459
This solution is correct!
Solution 3:
623, 342, 412
Verification:
(623 + 342 + 412) / 3 = 1377 / 3 ≈ 459
This solution is correct!
Solution 4:
719, 442, 216
Verification:
(719 + 442 + 216) / 3 = 1377 / 3 ≈ 459
This solution is correct!
Solution 5:
844, 511, 22
Verification:
(844 + 511 + 22) / 3 = 1377 / 3 ≈ 459
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 1377 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.