What three numbers have an average of 741?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 741. This means if we add these three numbers together and divide by 3, we should get 741.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 741 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 741 * 3 = x + y + z
- So, the sum of our three numbers should be: 2223
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2223.
Solution 1:
741, 741, 741
Verification:
(741 + 741 + 741) / 3 = 2223 / 3 ≈ 741
This solution is correct!
Solution 2:
741, 741, 741
Verification:
(741 + 741 + 741) / 3 = 2223 / 3 ≈ 741
This solution is correct!
Solution 3:
20, 1752, 451
Verification:
(20 + 1752 + 451) / 3 = 2223 / 3 ≈ 741
This solution is correct!
Solution 4:
2101, 102, 20
Verification:
(2101 + 102 + 20) / 3 = 2223 / 3 ≈ 741
This solution is correct!
Solution 5:
1538, 629, 56
Verification:
(1538 + 629 + 56) / 3 = 2223 / 3 ≈ 741
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 2223 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.