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:
832, 1414, 73
Verification:
(832 + 1414 + 73) / 3 = 2319 / 3 ≈ 773
This solution is correct!
Solution 4:
1635, 391, 293
Verification:
(1635 + 391 + 293) / 3 = 2319 / 3 ≈ 773
This solution is correct!
Solution 5:
1838, 79, 402
Verification:
(1838 + 79 + 402) / 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.