What three numbers have an average of 772?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 772. This means if we add these three numbers together and divide by 3, we should get 772.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 772 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 772 * 3 = x + y + z
- So, the sum of our three numbers should be: 2316
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2316.
Solution 1:
772, 772, 772
Verification:
(772 + 772 + 772) / 3 = 2316 / 3 ≈ 772
This solution is correct!
Solution 2:
772, 772, 772
Verification:
(772 + 772 + 772) / 3 = 2316 / 3 ≈ 772
This solution is correct!
Solution 3:
1385, 88, 843
Verification:
(1385 + 88 + 843) / 3 = 2316 / 3 ≈ 772
This solution is correct!
Solution 4:
1906, 298, 112
Verification:
(1906 + 298 + 112) / 3 = 2316 / 3 ≈ 772
This solution is correct!
Solution 5:
1550, 75, 691
Verification:
(1550 + 75 + 691) / 3 = 2316 / 3 ≈ 772
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 2316 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.