What three numbers have an average of 329?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 329. This means if we add these three numbers together and divide by 3, we should get 329.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 329 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 329 * 3 = x + y + z
- So, the sum of our three numbers should be: 987
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 987.
Solution 1:
329, 329, 329
Verification:
(329 + 329 + 329) / 3 = 987 / 3 ≈ 329
This solution is correct!
Solution 2:
329, 329, 329
Verification:
(329 + 329 + 329) / 3 = 987 / 3 ≈ 329
This solution is correct!
Solution 3:
146, 749, 92
Verification:
(146 + 749 + 92) / 3 = 987 / 3 ≈ 329
This solution is correct!
Solution 4:
740, 83, 164
Verification:
(740 + 83 + 164) / 3 = 987 / 3 ≈ 329
This solution is correct!
Solution 5:
929, 8, 50
Verification:
(929 + 8 + 50) / 3 = 987 / 3 ≈ 329
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 987 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.