What three numbers have an average of 232?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 232. This means if we add these three numbers together and divide by 3, we should get 232.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 232 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 232 * 3 = x + y + z
- So, the sum of our three numbers should be: 696
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 696.
Solution 1:
232, 232, 232
Verification:
(232 + 232 + 232) / 3 = 696 / 3 ≈ 232
This solution is correct!
Solution 2:
232, 232, 232
Verification:
(232 + 232 + 232) / 3 = 696 / 3 ≈ 232
This solution is correct!
Solution 3:
331, 284, 81
Verification:
(331 + 284 + 81) / 3 = 696 / 3 ≈ 232
This solution is correct!
Solution 4:
295, 3, 398
Verification:
(295 + 3 + 398) / 3 = 696 / 3 ≈ 232
This solution is correct!
Solution 5:
146, 352, 198
Verification:
(146 + 352 + 198) / 3 = 696 / 3 ≈ 232
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 696 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.