What three numbers have an average of 569?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 569. This means if we add these three numbers together and divide by 3, we should get 569.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 569 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 569 * 3 = x + y + z
- So, the sum of our three numbers should be: 1707
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1707.
Solution 1:
569, 569, 569
Verification:
(569 + 569 + 569) / 3 = 1707 / 3 ≈ 569
This solution is correct!
Solution 2:
569, 569, 569
Verification:
(569 + 569 + 569) / 3 = 1707 / 3 ≈ 569
This solution is correct!
Solution 3:
377, 36, 1294
Verification:
(377 + 36 + 1294) / 3 = 1707 / 3 ≈ 569
This solution is correct!
Solution 4:
155, 756, 796
Verification:
(155 + 756 + 796) / 3 = 1707 / 3 ≈ 569
This solution is correct!
Solution 5:
951, 370, 386
Verification:
(951 + 370 + 386) / 3 = 1707 / 3 ≈ 569
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 1707 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.