What three numbers have an average of 767?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 767. This means if we add these three numbers together and divide by 3, we should get 767.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 767 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 767 * 3 = x + y + z
- So, the sum of our three numbers should be: 2301
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2301.
Solution 1:
767, 767, 767
Verification:
(767 + 767 + 767) / 3 = 2301 / 3 ≈ 767
This solution is correct!
Solution 2:
767, 767, 767
Verification:
(767 + 767 + 767) / 3 = 2301 / 3 ≈ 767
This solution is correct!
Solution 3:
1531, 353, 417
Verification:
(1531 + 353 + 417) / 3 = 2301 / 3 ≈ 767
This solution is correct!
Solution 4:
1609, 485, 207
Verification:
(1609 + 485 + 207) / 3 = 2301 / 3 ≈ 767
This solution is correct!
Solution 5:
1580, 654, 67
Verification:
(1580 + 654 + 67) / 3 = 2301 / 3 ≈ 767
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 2301 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.