What three numbers have an average of 522?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 522. This means if we add these three numbers together and divide by 3, we should get 522.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 522 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 522 * 3 = x + y + z
- So, the sum of our three numbers should be: 1566
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1566.
Solution 1:
522, 522, 522
Verification:
(522 + 522 + 522) / 3 = 1566 / 3 ≈ 522
This solution is correct!
Solution 2:
522, 522, 522
Verification:
(522 + 522 + 522) / 3 = 1566 / 3 ≈ 522
This solution is correct!
Solution 3:
255, 1248, 63
Verification:
(255 + 1248 + 63) / 3 = 1566 / 3 ≈ 522
This solution is correct!
Solution 4:
405, 978, 183
Verification:
(405 + 978 + 183) / 3 = 1566 / 3 ≈ 522
This solution is correct!
Solution 5:
778, 331, 457
Verification:
(778 + 331 + 457) / 3 = 1566 / 3 ≈ 522
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 1566 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.