What three numbers have an average of 725?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 725. This means if we add these three numbers together and divide by 3, we should get 725.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 725 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 725 * 3 = x + y + z
- So, the sum of our three numbers should be: 2175
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2175.
Solution 1:
725, 725, 725
Verification:
(725 + 725 + 725) / 3 = 2175 / 3 ≈ 725
This solution is correct!
Solution 2:
725, 725, 725
Verification:
(725 + 725 + 725) / 3 = 2175 / 3 ≈ 725
This solution is correct!
Solution 3:
1397, 284, 494
Verification:
(1397 + 284 + 494) / 3 = 2175 / 3 ≈ 725
This solution is correct!
Solution 4:
1824, 22, 329
Verification:
(1824 + 22 + 329) / 3 = 2175 / 3 ≈ 725
This solution is correct!
Solution 5:
580, 1175, 420
Verification:
(580 + 1175 + 420) / 3 = 2175 / 3 ≈ 725
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 2175 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.