What three numbers have an average of 667?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 667. This means if we add these three numbers together and divide by 3, we should get 667.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 667 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 667 * 3 = x + y + z
- So, the sum of our three numbers should be: 2001
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2001.
Solution 1:
667, 667, 667
Verification:
(667 + 667 + 667) / 3 = 2001 / 3 ≈ 667
This solution is correct!
Solution 2:
667, 667, 667
Verification:
(667 + 667 + 667) / 3 = 2001 / 3 ≈ 667
This solution is correct!
Solution 3:
1429, 567, 5
Verification:
(1429 + 567 + 5) / 3 = 2001 / 3 ≈ 667
This solution is correct!
Solution 4:
812, 553, 636
Verification:
(812 + 553 + 636) / 3 = 2001 / 3 ≈ 667
This solution is correct!
Solution 5:
12, 189, 1800
Verification:
(12 + 189 + 1800) / 3 = 2001 / 3 ≈ 667
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 2001 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.