What three numbers have an average of 586?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 586. This means if we add these three numbers together and divide by 3, we should get 586.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 586 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 586 * 3 = x + y + z
- So, the sum of our three numbers should be: 1758
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1758.
Solution 1:
586, 586, 586
Verification:
(586 + 586 + 586) / 3 = 1758 / 3 ≈ 586
This solution is correct!
Solution 2:
586, 586, 586
Verification:
(586 + 586 + 586) / 3 = 1758 / 3 ≈ 586
This solution is correct!
Solution 3:
528, 594, 636
Verification:
(528 + 594 + 636) / 3 = 1758 / 3 ≈ 586
This solution is correct!
Solution 4:
19, 611, 1128
Verification:
(19 + 611 + 1128) / 3 = 1758 / 3 ≈ 586
This solution is correct!
Solution 5:
1387, 72, 299
Verification:
(1387 + 72 + 299) / 3 = 1758 / 3 ≈ 586
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 1758 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.