What three numbers have an average of 503?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 503. This means if we add these three numbers together and divide by 3, we should get 503.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 503 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 503 * 3 = x + y + z
- So, the sum of our three numbers should be: 1509
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1509.
Solution 1:
503, 503, 503
Verification:
(503 + 503 + 503) / 3 = 1509 / 3 ≈ 503
This solution is correct!
Solution 2:
503, 503, 503
Verification:
(503 + 503 + 503) / 3 = 1509 / 3 ≈ 503
This solution is correct!
Solution 3:
1139, 222, 148
Verification:
(1139 + 222 + 148) / 3 = 1509 / 3 ≈ 503
This solution is correct!
Solution 4:
1485, 17, 7
Verification:
(1485 + 17 + 7) / 3 = 1509 / 3 ≈ 503
This solution is correct!
Solution 5:
1153, 55, 301
Verification:
(1153 + 55 + 301) / 3 = 1509 / 3 ≈ 503
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 1509 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.