What three numbers have an average of 666?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 666. This means if we add these three numbers together and divide by 3, we should get 666.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 666 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 666 * 3 = x + y + z
- So, the sum of our three numbers should be: 1998
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1998.
Solution 1:
666, 666, 666
Verification:
(666 + 666 + 666) / 3 = 1998 / 3 ≈ 666
This solution is correct!
Solution 2:
666, 666, 666
Verification:
(666 + 666 + 666) / 3 = 1998 / 3 ≈ 666
This solution is correct!
Solution 3:
111, 1478, 409
Verification:
(111 + 1478 + 409) / 3 = 1998 / 3 ≈ 666
This solution is correct!
Solution 4:
93, 42, 1863
Verification:
(93 + 42 + 1863) / 3 = 1998 / 3 ≈ 666
This solution is correct!
Solution 5:
1662, 58, 278
Verification:
(1662 + 58 + 278) / 3 = 1998 / 3 ≈ 666
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 1998 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.