What three numbers have an average of 571?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 571. This means if we add these three numbers together and divide by 3, we should get 571.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 571 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 571 * 3 = x + y + z
- So, the sum of our three numbers should be: 1713
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1713.
Solution 1:
571, 571, 571
Verification:
(571 + 571 + 571) / 3 = 1713 / 3 ≈ 571
This solution is correct!
Solution 2:
571, 571, 571
Verification:
(571 + 571 + 571) / 3 = 1713 / 3 ≈ 571
This solution is correct!
Solution 3:
1242, 206, 265
Verification:
(1242 + 206 + 265) / 3 = 1713 / 3 ≈ 571
This solution is correct!
Solution 4:
1389, 219, 105
Verification:
(1389 + 219 + 105) / 3 = 1713 / 3 ≈ 571
This solution is correct!
Solution 5:
1194, 150, 369
Verification:
(1194 + 150 + 369) / 3 = 1713 / 3 ≈ 571
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 1713 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.