What three numbers have an average of 773?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 773. This means if we add these three numbers together and divide by 3, we should get 773.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 773 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 773 * 3 = x + y + z
- So, the sum of our three numbers should be: 2319
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2319.
Solution 1:
773, 773, 773
Verification:
(773 + 773 + 773) / 3 = 2319 / 3 ≈ 773
This solution is correct!
Solution 2:
773, 773, 773
Verification:
(773 + 773 + 773) / 3 = 2319 / 3 ≈ 773
This solution is correct!
Solution 3:
551, 1553, 215
Verification:
(551 + 1553 + 215) / 3 = 2319 / 3 ≈ 773
This solution is correct!
Solution 4:
2141, 134, 44
Verification:
(2141 + 134 + 44) / 3 = 2319 / 3 ≈ 773
This solution is correct!
Solution 5:
2198, 19, 102
Verification:
(2198 + 19 + 102) / 3 = 2319 / 3 ≈ 773
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 2319 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.