What three numbers have an average of 200?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 200. This means if we add these three numbers together and divide by 3, we should get 200.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 200 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 200 * 3 = x + y + z
- So, the sum of our three numbers should be: 600
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 600.
Solution 1:
200, 200, 200
Verification:
(200 + 200 + 200) / 3 = 600 / 3 ≈ 200
This solution is correct!
Solution 2:
200, 200, 200
Verification:
(200 + 200 + 200) / 3 = 600 / 3 ≈ 200
This solution is correct!
Solution 3:
485, 70, 45
Verification:
(485 + 70 + 45) / 3 = 600 / 3 ≈ 200
This solution is correct!
Solution 4:
341, 184, 75
Verification:
(341 + 184 + 75) / 3 = 600 / 3 ≈ 200
This solution is correct!
Solution 5:
171, 248, 181
Verification:
(171 + 248 + 181) / 3 = 600 / 3 ≈ 200
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 600 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.