What three numbers have an average of 492?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 492. This means if we add these three numbers together and divide by 3, we should get 492.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 492 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 492 * 3 = x + y + z
- So, the sum of our three numbers should be: 1476
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1476.
Solution 1:
492, 492, 492
Verification:
(492 + 492 + 492) / 3 = 1476 / 3 ≈ 492
This solution is correct!
Solution 2:
492, 492, 492
Verification:
(492 + 492 + 492) / 3 = 1476 / 3 ≈ 492
This solution is correct!
Solution 3:
1190, 82, 204
Verification:
(1190 + 82 + 204) / 3 = 1476 / 3 ≈ 492
This solution is correct!
Solution 4:
382, 663, 431
Verification:
(382 + 663 + 431) / 3 = 1476 / 3 ≈ 492
This solution is correct!
Solution 5:
1438, 16, 22
Verification:
(1438 + 16 + 22) / 3 = 1476 / 3 ≈ 492
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 1476 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.