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:
943, 814, 52
Verification:
(943 + 814 + 52) / 3 = 1809 / 3 ≈ 603
This solution is correct!
Solution 4:
322, 1317, 170
Verification:
(322 + 1317 + 170) / 3 = 1809 / 3 ≈ 603
This solution is correct!
Solution 5:
51, 551, 1207
Verification:
(51 + 551 + 1207) / 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.