What three numbers have an average of 501?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 501. This means if we add these three numbers together and divide by 3, we should get 501.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 501 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 501 * 3 = x + y + z
- So, the sum of our three numbers should be: 1503
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1503.
Solution 1:
501, 501, 501
Verification:
(501 + 501 + 501) / 3 = 1503 / 3 ≈ 501
This solution is correct!
Solution 2:
501, 501, 501
Verification:
(501 + 501 + 501) / 3 = 1503 / 3 ≈ 501
This solution is correct!
Solution 3:
1256, 173, 74
Verification:
(1256 + 173 + 74) / 3 = 1503 / 3 ≈ 501
This solution is correct!
Solution 4:
1075, 90, 338
Verification:
(1075 + 90 + 338) / 3 = 1503 / 3 ≈ 501
This solution is correct!
Solution 5:
51, 1084, 368
Verification:
(51 + 1084 + 368) / 3 = 1503 / 3 ≈ 501
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 1503 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.