What three numbers have an average of 171?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 171. This means if we add these three numbers together and divide by 3, we should get 171.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 171 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 171 * 3 = x + y + z
- So, the sum of our three numbers should be: 513
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 513.
Solution 1:
171, 171, 171
Verification:
(171 + 171 + 171) / 3 = 513 / 3 ≈ 171
This solution is correct!
Solution 2:
171, 171, 171
Verification:
(171 + 171 + 171) / 3 = 513 / 3 ≈ 171
This solution is correct!
Solution 3:
502, 1, 10
Verification:
(502 + 1 + 10) / 3 = 513 / 3 ≈ 171
This solution is correct!
Solution 4:
388, 55, 70
Verification:
(388 + 55 + 70) / 3 = 513 / 3 ≈ 171
This solution is correct!
Solution 5:
241, 262, 10
Verification:
(241 + 262 + 10) / 3 = 513 / 3 ≈ 171
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 513 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.