What three numbers have an average of 490?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 490. This means if we add these three numbers together and divide by 3, we should get 490.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 490 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 490 * 3 = x + y + z
- So, the sum of our three numbers should be: 1470
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1470.
Solution 1:
490, 490, 490
Verification:
(490 + 490 + 490) / 3 = 1470 / 3 ≈ 490
This solution is correct!
Solution 2:
490, 490, 490
Verification:
(490 + 490 + 490) / 3 = 1470 / 3 ≈ 490
This solution is correct!
Solution 3:
479, 684, 307
Verification:
(479 + 684 + 307) / 3 = 1470 / 3 ≈ 490
This solution is correct!
Solution 4:
1336, 76, 58
Verification:
(1336 + 76 + 58) / 3 = 1470 / 3 ≈ 490
This solution is correct!
Solution 5:
1455, 12, 3
Verification:
(1455 + 12 + 3) / 3 = 1470 / 3 ≈ 490
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 1470 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.