What three numbers have an average of 585?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 585. This means if we add these three numbers together and divide by 3, we should get 585.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 585 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 585 * 3 = x + y + z
- So, the sum of our three numbers should be: 1755
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1755.
Solution 1:
585, 585, 585
Verification:
(585 + 585 + 585) / 3 = 1755 / 3 ≈ 585
This solution is correct!
Solution 2:
585, 585, 585
Verification:
(585 + 585 + 585) / 3 = 1755 / 3 ≈ 585
This solution is correct!
Solution 3:
819, 485, 451
Verification:
(819 + 485 + 451) / 3 = 1755 / 3 ≈ 585
This solution is correct!
Solution 4:
244, 258, 1253
Verification:
(244 + 258 + 1253) / 3 = 1755 / 3 ≈ 585
This solution is correct!
Solution 5:
2, 605, 1148
Verification:
(2 + 605 + 1148) / 3 = 1755 / 3 ≈ 585
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 1755 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.