What three numbers have an average of 230?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 230. This means if we add these three numbers together and divide by 3, we should get 230.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 230 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 230 * 3 = x + y + z
- So, the sum of our three numbers should be: 690
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 690.
Solution 1:
230, 230, 230
Verification:
(230 + 230 + 230) / 3 = 690 / 3 ≈ 230
This solution is correct!
Solution 2:
230, 230, 230
Verification:
(230 + 230 + 230) / 3 = 690 / 3 ≈ 230
This solution is correct!
Solution 3:
546, 97, 47
Verification:
(546 + 97 + 47) / 3 = 690 / 3 ≈ 230
This solution is correct!
Solution 4:
71, 51, 568
Verification:
(71 + 51 + 568) / 3 = 690 / 3 ≈ 230
This solution is correct!
Solution 5:
518, 15, 157
Verification:
(518 + 15 + 157) / 3 = 690 / 3 ≈ 230
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 690 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.