What three numbers have an average of 592?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 592. This means if we add these three numbers together and divide by 3, we should get 592.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 592 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 592 * 3 = x + y + z
- So, the sum of our three numbers should be: 1776
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1776.
Solution 1:
592, 592, 592
Verification:
(592 + 592 + 592) / 3 = 1776 / 3 ≈ 592
This solution is correct!
Solution 2:
592, 592, 592
Verification:
(592 + 592 + 592) / 3 = 1776 / 3 ≈ 592
This solution is correct!
Solution 3:
1699, 28, 49
Verification:
(1699 + 28 + 49) / 3 = 1776 / 3 ≈ 592
This solution is correct!
Solution 4:
1358, 249, 169
Verification:
(1358 + 249 + 169) / 3 = 1776 / 3 ≈ 592
This solution is correct!
Solution 5:
1218, 162, 396
Verification:
(1218 + 162 + 396) / 3 = 1776 / 3 ≈ 592
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 1776 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.