What three numbers have an average of 238?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 238. This means if we add these three numbers together and divide by 3, we should get 238.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 238 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 238 * 3 = x + y + z
- So, the sum of our three numbers should be: 714
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 714.
Solution 1:
238, 238, 238
Verification:
(238 + 238 + 238) / 3 = 714 / 3 ≈ 238
This solution is correct!
Solution 2:
238, 238, 238
Verification:
(238 + 238 + 238) / 3 = 714 / 3 ≈ 238
This solution is correct!
Solution 3:
458, 178, 78
Verification:
(458 + 178 + 78) / 3 = 714 / 3 ≈ 238
This solution is correct!
Solution 4:
427, 213, 74
Verification:
(427 + 213 + 74) / 3 = 714 / 3 ≈ 238
This solution is correct!
Solution 5:
291, 15, 408
Verification:
(291 + 15 + 408) / 3 = 714 / 3 ≈ 238
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 714 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.