What three numbers have an average of 203?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 203. This means if we add these three numbers together and divide by 3, we should get 203.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 203 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 203 * 3 = x + y + z
- So, the sum of our three numbers should be: 609
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 609.
Solution 1:
203, 203, 203
Verification:
(203 + 203 + 203) / 3 = 609 / 3 ≈ 203
This solution is correct!
Solution 2:
203, 203, 203
Verification:
(203 + 203 + 203) / 3 = 609 / 3 ≈ 203
This solution is correct!
Solution 3:
512, 87, 10
Verification:
(512 + 87 + 10) / 3 = 609 / 3 ≈ 203
This solution is correct!
Solution 4:
458, 52, 99
Verification:
(458 + 52 + 99) / 3 = 609 / 3 ≈ 203
This solution is correct!
Solution 5:
315, 97, 197
Verification:
(315 + 97 + 197) / 3 = 609 / 3 ≈ 203
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 609 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.