What three numbers have an average of 603?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 603. This means if we add these three numbers together and divide by 3, we should get 603.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 603 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 603 * 3 = x + y + z
- So, the sum of our three numbers should be: 1809
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1809.
Solution 1:
603, 603, 603
Verification:
(603 + 603 + 603) / 3 = 1809 / 3 ≈ 603
This solution is correct!
Solution 2:
603, 603, 603
Verification:
(603 + 603 + 603) / 3 = 1809 / 3 ≈ 603
This solution is correct!
Solution 3:
174, 1186, 449
Verification:
(174 + 1186 + 449) / 3 = 1809 / 3 ≈ 603
This solution is correct!
Solution 4:
345, 649, 815
Verification:
(345 + 649 + 815) / 3 = 1809 / 3 ≈ 603
This solution is correct!
Solution 5:
1152, 362, 295
Verification:
(1152 + 362 + 295) / 3 = 1809 / 3 ≈ 603
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 1809 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.