What three numbers have an average of 174?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 174. This means if we add these three numbers together and divide by 3, we should get 174.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 174 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 174 * 3 = x + y + z
- So, the sum of our three numbers should be: 522
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 522.
Solution 1:
174, 174, 174
Verification:
(174 + 174 + 174) / 3 = 522 / 3 ≈ 174
This solution is correct!
Solution 2:
174, 174, 174
Verification:
(174 + 174 + 174) / 3 = 522 / 3 ≈ 174
This solution is correct!
Solution 3:
192, 240, 90
Verification:
(192 + 240 + 90) / 3 = 522 / 3 ≈ 174
This solution is correct!
Solution 4:
326, 123, 73
Verification:
(326 + 123 + 73) / 3 = 522 / 3 ≈ 174
This solution is correct!
Solution 5:
16, 199, 307
Verification:
(16 + 199 + 307) / 3 = 522 / 3 ≈ 174
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 522 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.