What three numbers have an average of 578?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 578. This means if we add these three numbers together and divide by 3, we should get 578.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 578 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 578 * 3 = x + y + z
- So, the sum of our three numbers should be: 1734
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1734.
Solution 1:
578, 578, 578
Verification:
(578 + 578 + 578) / 3 = 1734 / 3 ≈ 578
This solution is correct!
Solution 2:
578, 578, 578
Verification:
(578 + 578 + 578) / 3 = 1734 / 3 ≈ 578
This solution is correct!
Solution 3:
503, 290, 941
Verification:
(503 + 290 + 941) / 3 = 1734 / 3 ≈ 578
This solution is correct!
Solution 4:
1192, 287, 255
Verification:
(1192 + 287 + 255) / 3 = 1734 / 3 ≈ 578
This solution is correct!
Solution 5:
959, 190, 585
Verification:
(959 + 190 + 585) / 3 = 1734 / 3 ≈ 578
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 1734 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.