What three numbers have an average of 757?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 757. This means if we add these three numbers together and divide by 3, we should get 757.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 757 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 757 * 3 = x + y + z
- So, the sum of our three numbers should be: 2271
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2271.
Solution 1:
757, 757, 757
Verification:
(757 + 757 + 757) / 3 = 2271 / 3 ≈ 757
This solution is correct!
Solution 2:
757, 757, 757
Verification:
(757 + 757 + 757) / 3 = 2271 / 3 ≈ 757
This solution is correct!
Solution 3:
971, 1171, 129
Verification:
(971 + 1171 + 129) / 3 = 2271 / 3 ≈ 757
This solution is correct!
Solution 4:
1849, 21, 401
Verification:
(1849 + 21 + 401) / 3 = 2271 / 3 ≈ 757
This solution is correct!
Solution 5:
498, 103, 1670
Verification:
(498 + 103 + 1670) / 3 = 2271 / 3 ≈ 757
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 2271 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.