What three numbers have an average of 598?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 598. This means if we add these three numbers together and divide by 3, we should get 598.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 598 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 598 * 3 = x + y + z
- So, the sum of our three numbers should be: 1794
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1794.
Solution 1:
598, 598, 598
Verification:
(598 + 598 + 598) / 3 = 1794 / 3 ≈ 598
This solution is correct!
Solution 2:
598, 598, 598
Verification:
(598 + 598 + 598) / 3 = 1794 / 3 ≈ 598
This solution is correct!
Solution 3:
573, 889, 332
Verification:
(573 + 889 + 332) / 3 = 1794 / 3 ≈ 598
This solution is correct!
Solution 4:
934, 315, 545
Verification:
(934 + 315 + 545) / 3 = 1794 / 3 ≈ 598
This solution is correct!
Solution 5:
196, 1426, 172
Verification:
(196 + 1426 + 172) / 3 = 1794 / 3 ≈ 598
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 1794 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.