What three numbers have an average of 206?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 206. This means if we add these three numbers together and divide by 3, we should get 206.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 206 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 206 * 3 = x + y + z
- So, the sum of our three numbers should be: 618
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 618.
Solution 1:
206, 206, 206
Verification:
(206 + 206 + 206) / 3 = 618 / 3 ≈ 206
This solution is correct!
Solution 2:
206, 206, 206
Verification:
(206 + 206 + 206) / 3 = 618 / 3 ≈ 206
This solution is correct!
Solution 3:
502, 114, 2
Verification:
(502 + 114 + 2) / 3 = 618 / 3 ≈ 206
This solution is correct!
Solution 4:
169, 102, 347
Verification:
(169 + 102 + 347) / 3 = 618 / 3 ≈ 206
This solution is correct!
Solution 5:
588, 23, 7
Verification:
(588 + 23 + 7) / 3 = 618 / 3 ≈ 206
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 618 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.