What three numbers have an average of 568?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 568. This means if we add these three numbers together and divide by 3, we should get 568.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 568 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 568 * 3 = x + y + z
- So, the sum of our three numbers should be: 1704
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1704.
Solution 1:
568, 568, 568
Verification:
(568 + 568 + 568) / 3 = 1704 / 3 ≈ 568
This solution is correct!
Solution 2:
568, 568, 568
Verification:
(568 + 568 + 568) / 3 = 1704 / 3 ≈ 568
This solution is correct!
Solution 3:
888, 610, 206
Verification:
(888 + 610 + 206) / 3 = 1704 / 3 ≈ 568
This solution is correct!
Solution 4:
974, 336, 394
Verification:
(974 + 336 + 394) / 3 = 1704 / 3 ≈ 568
This solution is correct!
Solution 5:
869, 422, 413
Verification:
(869 + 422 + 413) / 3 = 1704 / 3 ≈ 568
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 1704 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.