What three numbers have an average of 494?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 494. This means if we add these three numbers together and divide by 3, we should get 494.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 494 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 494 * 3 = x + y + z
- So, the sum of our three numbers should be: 1482
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1482.
Solution 1:
494, 494, 494
Verification:
(494 + 494 + 494) / 3 = 1482 / 3 ≈ 494
This solution is correct!
Solution 2:
494, 494, 494
Verification:
(494 + 494 + 494) / 3 = 1482 / 3 ≈ 494
This solution is correct!
Solution 3:
1109, 114, 259
Verification:
(1109 + 114 + 259) / 3 = 1482 / 3 ≈ 494
This solution is correct!
Solution 4:
1425, 8, 49
Verification:
(1425 + 8 + 49) / 3 = 1482 / 3 ≈ 494
This solution is correct!
Solution 5:
642, 762, 78
Verification:
(642 + 762 + 78) / 3 = 1482 / 3 ≈ 494
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 1482 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.