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:
1421, 53, 38
Verification:
(1421 + 53 + 38) / 3 = 1512 / 3 ≈ 504
This solution is correct!
Solution 4:
1420, 40, 52
Verification:
(1420 + 40 + 52) / 3 = 1512 / 3 ≈ 504
This solution is correct!
Solution 5:
1477, 2, 33
Verification:
(1477 + 2 + 33) / 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.