What three numbers have an average of 231?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 231. This means if we add these three numbers together and divide by 3, we should get 231.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 231 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 231 * 3 = x + y + z
- So, the sum of our three numbers should be: 693
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 693.
Solution 1:
231, 231, 231
Verification:
(231 + 231 + 231) / 3 = 693 / 3 ≈ 231
This solution is correct!
Solution 2:
231, 231, 231
Verification:
(231 + 231 + 231) / 3 = 693 / 3 ≈ 231
This solution is correct!
Solution 3:
176, 60, 457
Verification:
(176 + 60 + 457) / 3 = 693 / 3 ≈ 231
This solution is correct!
Solution 4:
496, 83, 114
Verification:
(496 + 83 + 114) / 3 = 693 / 3 ≈ 231
This solution is correct!
Solution 5:
346, 107, 240
Verification:
(346 + 107 + 240) / 3 = 693 / 3 ≈ 231
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 693 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.