What three numbers have an average of 205?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 205. This means if we add these three numbers together and divide by 3, we should get 205.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 205 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 205 * 3 = x + y + z
- So, the sum of our three numbers should be: 615
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 615.
Solution 1:
205, 205, 205
Verification:
(205 + 205 + 205) / 3 = 615 / 3 ≈ 205
This solution is correct!
Solution 2:
205, 205, 205
Verification:
(205 + 205 + 205) / 3 = 615 / 3 ≈ 205
This solution is correct!
Solution 3:
96, 428, 91
Verification:
(96 + 428 + 91) / 3 = 615 / 3 ≈ 205
This solution is correct!
Solution 4:
75, 155, 385
Verification:
(75 + 155 + 385) / 3 = 615 / 3 ≈ 205
This solution is correct!
Solution 5:
112, 105, 398
Verification:
(112 + 105 + 398) / 3 = 615 / 3 ≈ 205
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 615 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.