What three numbers have an average of 580?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 580. This means if we add these three numbers together and divide by 3, we should get 580.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 580 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 580 * 3 = x + y + z
- So, the sum of our three numbers should be: 1740
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1740.
Solution 1:
580, 580, 580
Verification:
(580 + 580 + 580) / 3 = 1740 / 3 ≈ 580
This solution is correct!
Solution 2:
580, 580, 580
Verification:
(580 + 580 + 580) / 3 = 1740 / 3 ≈ 580
This solution is correct!
Solution 3:
1318, 416, 6
Verification:
(1318 + 416 + 6) / 3 = 1740 / 3 ≈ 580
This solution is correct!
Solution 4:
592, 919, 229
Verification:
(592 + 919 + 229) / 3 = 1740 / 3 ≈ 580
This solution is correct!
Solution 5:
800, 139, 801
Verification:
(800 + 139 + 801) / 3 = 1740 / 3 ≈ 580
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 1740 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.