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:
502, 179, 1494
Verification:
(502 + 179 + 1494) / 3 = 2175 / 3 ≈ 725
This solution is correct!
Solution 4:
1427, 439, 309
Verification:
(1427 + 439 + 309) / 3 = 2175 / 3 ≈ 725
This solution is correct!
Solution 5:
1856, 131, 188
Verification:
(1856 + 131 + 188) / 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.