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:
731, 105, 541
Verification:
(731 + 105 + 541) / 3 = 1377 / 3 ≈ 459
This solution is correct!
Solution 4:
1001, 155, 221
Verification:
(1001 + 155 + 221) / 3 = 1377 / 3 ≈ 459
This solution is correct!
Solution 5:
964, 57, 356
Verification:
(964 + 57 + 356) / 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.