What three numbers have an average of 595?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 595. This means if we add these three numbers together and divide by 3, we should get 595.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 595 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 595 * 3 = x + y + z
- So, the sum of our three numbers should be: 1785
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1785.
Solution 1:
595, 595, 595
Verification:
(595 + 595 + 595) / 3 = 1785 / 3 ≈ 595
This solution is correct!
Solution 2:
595, 595, 595
Verification:
(595 + 595 + 595) / 3 = 1785 / 3 ≈ 595
This solution is correct!
Solution 3:
1538, 231, 16
Verification:
(1538 + 231 + 16) / 3 = 1785 / 3 ≈ 595
This solution is correct!
Solution 4:
1634, 32, 119
Verification:
(1634 + 32 + 119) / 3 = 1785 / 3 ≈ 595
This solution is correct!
Solution 5:
1429, 322, 34
Verification:
(1429 + 322 + 34) / 3 = 1785 / 3 ≈ 595
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 1785 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.