What three numbers have an average of 521?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 521. This means if we add these three numbers together and divide by 3, we should get 521.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 521 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 521 * 3 = x + y + z
- So, the sum of our three numbers should be: 1563
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1563.
Solution 1:
521, 521, 521
Verification:
(521 + 521 + 521) / 3 = 1563 / 3 ≈ 521
This solution is correct!
Solution 2:
521, 521, 521
Verification:
(521 + 521 + 521) / 3 = 1563 / 3 ≈ 521
This solution is correct!
Solution 3:
143, 850, 570
Verification:
(143 + 850 + 570) / 3 = 1563 / 3 ≈ 521
This solution is correct!
Solution 4:
174, 184, 1205
Verification:
(174 + 184 + 1205) / 3 = 1563 / 3 ≈ 521
This solution is correct!
Solution 5:
815, 281, 467
Verification:
(815 + 281 + 467) / 3 = 1563 / 3 ≈ 521
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 1563 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.