What three numbers have an average of 570?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 570. This means if we add these three numbers together and divide by 3, we should get 570.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 570 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 570 * 3 = x + y + z
- So, the sum of our three numbers should be: 1710
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1710.
Solution 1:
570, 570, 570
Verification:
(570 + 570 + 570) / 3 = 1710 / 3 ≈ 570
This solution is correct!
Solution 2:
570, 570, 570
Verification:
(570 + 570 + 570) / 3 = 1710 / 3 ≈ 570
This solution is correct!
Solution 3:
1243, 77, 390
Verification:
(1243 + 77 + 390) / 3 = 1710 / 3 ≈ 570
This solution is correct!
Solution 4:
1027, 653, 30
Verification:
(1027 + 653 + 30) / 3 = 1710 / 3 ≈ 570
This solution is correct!
Solution 5:
1706, 3, 1
Verification:
(1706 + 3 + 1) / 3 = 1710 / 3 ≈ 570
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 1710 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.