What three numbers have an average of 161?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 161. This means if we add these three numbers together and divide by 3, we should get 161.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 161 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 161 * 3 = x + y + z
- So, the sum of our three numbers should be: 483
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 483.
Solution 1:
161, 161, 161
Verification:
(161 + 161 + 161) / 3 = 483 / 3 ≈ 161
This solution is correct!
Solution 2:
161, 161, 161
Verification:
(161 + 161 + 161) / 3 = 483 / 3 ≈ 161
This solution is correct!
Solution 3:
253, 145, 85
Verification:
(253 + 145 + 85) / 3 = 483 / 3 ≈ 161
This solution is correct!
Solution 4:
6, 273, 204
Verification:
(6 + 273 + 204) / 3 = 483 / 3 ≈ 161
This solution is correct!
Solution 5:
392, 23, 68
Verification:
(392 + 23 + 68) / 3 = 483 / 3 ≈ 161
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 483 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.