What three numbers have an average of 258?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 258. This means if we add these three numbers together and divide by 3, we should get 258.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 258 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 258 * 3 = x + y + z
- So, the sum of our three numbers should be: 774
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 774.
Solution 1:
258, 258, 258
Verification:
(258 + 258 + 258) / 3 = 774 / 3 ≈ 258
This solution is correct!
Solution 2:
258, 258, 258
Verification:
(258 + 258 + 258) / 3 = 774 / 3 ≈ 258
This solution is correct!
Solution 3:
565, 139, 70
Verification:
(565 + 139 + 70) / 3 = 774 / 3 ≈ 258
This solution is correct!
Solution 4:
527, 9, 238
Verification:
(527 + 9 + 238) / 3 = 774 / 3 ≈ 258
This solution is correct!
Solution 5:
569, 122, 83
Verification:
(569 + 122 + 83) / 3 = 774 / 3 ≈ 258
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 774 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.