What three numbers have an average of 777?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 777. This means if we add these three numbers together and divide by 3, we should get 777.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 777 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 777 * 3 = x + y + z
- So, the sum of our three numbers should be: 2331
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2331.
Solution 1:
777, 777, 777
Verification:
(777 + 777 + 777) / 3 = 2331 / 3 ≈ 777
This solution is correct!
Solution 2:
777, 777, 777
Verification:
(777 + 777 + 777) / 3 = 2331 / 3 ≈ 777
This solution is correct!
Solution 3:
253, 1073, 1005
Verification:
(253 + 1073 + 1005) / 3 = 2331 / 3 ≈ 777
This solution is correct!
Solution 4:
2207, 24, 100
Verification:
(2207 + 24 + 100) / 3 = 2331 / 3 ≈ 777
This solution is correct!
Solution 5:
1177, 27, 1127
Verification:
(1177 + 27 + 1127) / 3 = 2331 / 3 ≈ 777
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 2331 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.