What three numbers have an average of 507?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 507. This means if we add these three numbers together and divide by 3, we should get 507.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 507 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 507 * 3 = x + y + z
- So, the sum of our three numbers should be: 1521
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1521.
Solution 1:
507, 507, 507
Verification:
(507 + 507 + 507) / 3 = 1521 / 3 ≈ 507
This solution is correct!
Solution 2:
507, 507, 507
Verification:
(507 + 507 + 507) / 3 = 1521 / 3 ≈ 507
This solution is correct!
Solution 3:
1215, 227, 79
Verification:
(1215 + 227 + 79) / 3 = 1521 / 3 ≈ 507
This solution is correct!
Solution 4:
369, 412, 740
Verification:
(369 + 412 + 740) / 3 = 1521 / 3 ≈ 507
This solution is correct!
Solution 5:
585, 764, 172
Verification:
(585 + 764 + 172) / 3 = 1521 / 3 ≈ 507
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 1521 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.