What three numbers have an average of 669?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 669. This means if we add these three numbers together and divide by 3, we should get 669.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 669 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 669 * 3 = x + y + z
- So, the sum of our three numbers should be: 2007
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2007.
Solution 1:
669, 669, 669
Verification:
(669 + 669 + 669) / 3 = 2007 / 3 ≈ 669
This solution is correct!
Solution 2:
669, 669, 669
Verification:
(669 + 669 + 669) / 3 = 2007 / 3 ≈ 669
This solution is correct!
Solution 3:
1871, 58, 78
Verification:
(1871 + 58 + 78) / 3 = 2007 / 3 ≈ 669
This solution is correct!
Solution 4:
1821, 121, 65
Verification:
(1821 + 121 + 65) / 3 = 2007 / 3 ≈ 669
This solution is correct!
Solution 5:
887, 327, 793
Verification:
(887 + 327 + 793) / 3 = 2007 / 3 ≈ 669
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 2007 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.