What three numbers have an average of 176?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 176. This means if we add these three numbers together and divide by 3, we should get 176.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 176 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 176 * 3 = x + y + z
- So, the sum of our three numbers should be: 528
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 528.
Solution 1:
176, 176, 176
Verification:
(176 + 176 + 176) / 3 = 528 / 3 ≈ 176
This solution is correct!
Solution 2:
176, 176, 176
Verification:
(176 + 176 + 176) / 3 = 528 / 3 ≈ 176
This solution is correct!
Solution 3:
411, 71, 46
Verification:
(411 + 71 + 46) / 3 = 528 / 3 ≈ 176
This solution is correct!
Solution 4:
144, 129, 255
Verification:
(144 + 129 + 255) / 3 = 528 / 3 ≈ 176
This solution is correct!
Solution 5:
65, 260, 203
Verification:
(65 + 260 + 203) / 3 = 528 / 3 ≈ 176
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 528 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.