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:
1606, 90, 305
Verification:
(1606 + 90 + 305) / 3 = 2001 / 3 ≈ 667
This solution is correct!
Solution 4:
1473, 60, 468
Verification:
(1473 + 60 + 468) / 3 = 2001 / 3 ≈ 667
This solution is correct!
Solution 5:
825, 1118, 58
Verification:
(825 + 1118 + 58) / 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.