What three numbers have an average of 720?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 720. This means if we add these three numbers together and divide by 3, we should get 720.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 720 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 720 * 3 = x + y + z
- So, the sum of our three numbers should be: 2160
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2160.
Solution 1:
720, 720, 720
Verification:
(720 + 720 + 720) / 3 = 2160 / 3 ≈ 720
This solution is correct!
Solution 2:
720, 720, 720
Verification:
(720 + 720 + 720) / 3 = 2160 / 3 ≈ 720
This solution is correct!
Solution 3:
553, 785, 822
Verification:
(553 + 785 + 822) / 3 = 2160 / 3 ≈ 720
This solution is correct!
Solution 4:
1264, 750, 146
Verification:
(1264 + 750 + 146) / 3 = 2160 / 3 ≈ 720
This solution is correct!
Solution 5:
174, 734, 1252
Verification:
(174 + 734 + 1252) / 3 = 2160 / 3 ≈ 720
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 2160 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.