What three numbers have an average of 582?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 582. This means if we add these three numbers together and divide by 3, we should get 582.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 582 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 582 * 3 = x + y + z
- So, the sum of our three numbers should be: 1746
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1746.
Solution 1:
582, 582, 582
Verification:
(582 + 582 + 582) / 3 = 1746 / 3 ≈ 582
This solution is correct!
Solution 2:
582, 582, 582
Verification:
(582 + 582 + 582) / 3 = 1746 / 3 ≈ 582
This solution is correct!
Solution 3:
161, 724, 861
Verification:
(161 + 724 + 861) / 3 = 1746 / 3 ≈ 582
This solution is correct!
Solution 4:
1281, 202, 263
Verification:
(1281 + 202 + 263) / 3 = 1746 / 3 ≈ 582
This solution is correct!
Solution 5:
430, 727, 589
Verification:
(430 + 727 + 589) / 3 = 1746 / 3 ≈ 582
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 1746 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.