What three numbers have an average of 499?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 499. This means if we add these three numbers together and divide by 3, we should get 499.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 499 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 499 * 3 = x + y + z
- So, the sum of our three numbers should be: 1497
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1497.
Solution 1:
499, 499, 499
Verification:
(499 + 499 + 499) / 3 = 1497 / 3 ≈ 499
This solution is correct!
Solution 2:
499, 499, 499
Verification:
(499 + 499 + 499) / 3 = 1497 / 3 ≈ 499
This solution is correct!
Solution 3:
10, 1291, 196
Verification:
(10 + 1291 + 196) / 3 = 1497 / 3 ≈ 499
This solution is correct!
Solution 4:
247, 618, 632
Verification:
(247 + 618 + 632) / 3 = 1497 / 3 ≈ 499
This solution is correct!
Solution 5:
1308, 160, 29
Verification:
(1308 + 160 + 29) / 3 = 1497 / 3 ≈ 499
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 1497 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.