What three numbers have an average of 597?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 597. This means if we add these three numbers together and divide by 3, we should get 597.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 597 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 597 * 3 = x + y + z
- So, the sum of our three numbers should be: 1791
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1791.
Solution 1:
597, 597, 597
Verification:
(597 + 597 + 597) / 3 = 1791 / 3 ≈ 597
This solution is correct!
Solution 2:
597, 597, 597
Verification:
(597 + 597 + 597) / 3 = 1791 / 3 ≈ 597
This solution is correct!
Solution 3:
1160, 93, 538
Verification:
(1160 + 93 + 538) / 3 = 1791 / 3 ≈ 597
This solution is correct!
Solution 4:
394, 128, 1269
Verification:
(394 + 128 + 1269) / 3 = 1791 / 3 ≈ 597
This solution is correct!
Solution 5:
1479, 196, 116
Verification:
(1479 + 196 + 116) / 3 = 1791 / 3 ≈ 597
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 1791 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.