What three numbers have an average of 665?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 665. This means if we add these three numbers together and divide by 3, we should get 665.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 665 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 665 * 3 = x + y + z
- So, the sum of our three numbers should be: 1995
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1995.
Solution 1:
665, 665, 665
Verification:
(665 + 665 + 665) / 3 = 1995 / 3 ≈ 665
This solution is correct!
Solution 2:
665, 665, 665
Verification:
(665 + 665 + 665) / 3 = 1995 / 3 ≈ 665
This solution is correct!
Solution 3:
1667, 190, 138
Verification:
(1667 + 190 + 138) / 3 = 1995 / 3 ≈ 665
This solution is correct!
Solution 4:
107, 1569, 319
Verification:
(107 + 1569 + 319) / 3 = 1995 / 3 ≈ 665
This solution is correct!
Solution 5:
1506, 33, 456
Verification:
(1506 + 33 + 456) / 3 = 1995 / 3 ≈ 665
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 1995 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.