What three numbers have an average of 527?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 527. This means if we add these three numbers together and divide by 3, we should get 527.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 527 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 527 * 3 = x + y + z
- So, the sum of our three numbers should be: 1581
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1581.
Solution 1:
527, 527, 527
Verification:
(527 + 527 + 527) / 3 = 1581 / 3 ≈ 527
This solution is correct!
Solution 2:
527, 527, 527
Verification:
(527 + 527 + 527) / 3 = 1581 / 3 ≈ 527
This solution is correct!
Solution 3:
1103, 361, 117
Verification:
(1103 + 361 + 117) / 3 = 1581 / 3 ≈ 527
This solution is correct!
Solution 4:
1042, 382, 157
Verification:
(1042 + 382 + 157) / 3 = 1581 / 3 ≈ 527
This solution is correct!
Solution 5:
38, 1467, 76
Verification:
(38 + 1467 + 76) / 3 = 1581 / 3 ≈ 527
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 1581 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.