What three numbers have an average of 485?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 485. This means if we add these three numbers together and divide by 3, we should get 485.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 485 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 485 * 3 = x + y + z
- So, the sum of our three numbers should be: 1455
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1455.
Solution 1:
485, 485, 485
Verification:
(485 + 485 + 485) / 3 = 1455 / 3 ≈ 485
This solution is correct!
Solution 2:
485, 485, 485
Verification:
(485 + 485 + 485) / 3 = 1455 / 3 ≈ 485
This solution is correct!
Solution 3:
850, 270, 335
Verification:
(850 + 270 + 335) / 3 = 1455 / 3 ≈ 485
This solution is correct!
Solution 4:
1331, 74, 50
Verification:
(1331 + 74 + 50) / 3 = 1455 / 3 ≈ 485
This solution is correct!
Solution 5:
1196, 159, 100
Verification:
(1196 + 159 + 100) / 3 = 1455 / 3 ≈ 485
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 1455 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.