What three numbers have an average of 495?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 495. This means if we add these three numbers together and divide by 3, we should get 495.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 495 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 495 * 3 = x + y + z
- So, the sum of our three numbers should be: 1485
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1485.
Solution 1:
495, 495, 495
Verification:
(495 + 495 + 495) / 3 = 1485 / 3 ≈ 495
This solution is correct!
Solution 2:
495, 495, 495
Verification:
(495 + 495 + 495) / 3 = 1485 / 3 ≈ 495
This solution is correct!
Solution 3:
384, 268, 833
Verification:
(384 + 268 + 833) / 3 = 1485 / 3 ≈ 495
This solution is correct!
Solution 4:
182, 440, 863
Verification:
(182 + 440 + 863) / 3 = 1485 / 3 ≈ 495
This solution is correct!
Solution 5:
1401, 2, 82
Verification:
(1401 + 2 + 82) / 3 = 1485 / 3 ≈ 495
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 1485 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.