What three numbers have an average of 755?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 755. This means if we add these three numbers together and divide by 3, we should get 755.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 755 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 755 * 3 = x + y + z
- So, the sum of our three numbers should be: 2265
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2265.
Solution 1:
755, 755, 755
Verification:
(755 + 755 + 755) / 3 = 2265 / 3 ≈ 755
This solution is correct!
Solution 2:
755, 755, 755
Verification:
(755 + 755 + 755) / 3 = 2265 / 3 ≈ 755
This solution is correct!
Solution 3:
1995, 74, 196
Verification:
(1995 + 74 + 196) / 3 = 2265 / 3 ≈ 755
This solution is correct!
Solution 4:
1064, 186, 1015
Verification:
(1064 + 186 + 1015) / 3 = 2265 / 3 ≈ 755
This solution is correct!
Solution 5:
144, 1483, 638
Verification:
(144 + 1483 + 638) / 3 = 2265 / 3 ≈ 755
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 2265 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.