What three numbers have an average of 504?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 504. This means if we add these three numbers together and divide by 3, we should get 504.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 504 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 504 * 3 = x + y + z
- So, the sum of our three numbers should be: 1512
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1512.
Solution 1:
504, 504, 504
Verification:
(504 + 504 + 504) / 3 = 1512 / 3 ≈ 504
This solution is correct!
Solution 2:
504, 504, 504
Verification:
(504 + 504 + 504) / 3 = 1512 / 3 ≈ 504
This solution is correct!
Solution 3:
1357, 124, 31
Verification:
(1357 + 124 + 31) / 3 = 1512 / 3 ≈ 504
This solution is correct!
Solution 4:
856, 404, 252
Verification:
(856 + 404 + 252) / 3 = 1512 / 3 ≈ 504
This solution is correct!
Solution 5:
52, 921, 539
Verification:
(52 + 921 + 539) / 3 = 1512 / 3 ≈ 504
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 1512 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.