What three numbers have an average of 530?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 530. This means if we add these three numbers together and divide by 3, we should get 530.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 530 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 530 * 3 = x + y + z
- So, the sum of our three numbers should be: 1590
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1590.
Solution 1:
530, 530, 530
Verification:
(530 + 530 + 530) / 3 = 1590 / 3 ≈ 530
This solution is correct!
Solution 2:
530, 530, 530
Verification:
(530 + 530 + 530) / 3 = 1590 / 3 ≈ 530
This solution is correct!
Solution 3:
1373, 109, 108
Verification:
(1373 + 109 + 108) / 3 = 1590 / 3 ≈ 530
This solution is correct!
Solution 4:
1054, 416, 120
Verification:
(1054 + 416 + 120) / 3 = 1590 / 3 ≈ 530
This solution is correct!
Solution 5:
54, 1407, 129
Verification:
(54 + 1407 + 129) / 3 = 1590 / 3 ≈ 530
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 1590 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.