What three numbers have an average of 584?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 584. This means if we add these three numbers together and divide by 3, we should get 584.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 584 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 584 * 3 = x + y + z
- So, the sum of our three numbers should be: 1752
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1752.
Solution 1:
584, 584, 584
Verification:
(584 + 584 + 584) / 3 = 1752 / 3 ≈ 584
This solution is correct!
Solution 2:
584, 584, 584
Verification:
(584 + 584 + 584) / 3 = 1752 / 3 ≈ 584
This solution is correct!
Solution 3:
939, 106, 707
Verification:
(939 + 106 + 707) / 3 = 1752 / 3 ≈ 584
This solution is correct!
Solution 4:
482, 366, 904
Verification:
(482 + 366 + 904) / 3 = 1752 / 3 ≈ 584
This solution is correct!
Solution 5:
1478, 81, 193
Verification:
(1478 + 81 + 193) / 3 = 1752 / 3 ≈ 584
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 1752 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.