What three numbers have an average of 287?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 287. This means if we add these three numbers together and divide by 3, we should get 287.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 287 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 287 * 3 = x + y + z
- So, the sum of our three numbers should be: 861
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 861.
Solution 1:
287, 287, 287
Verification:
(287 + 287 + 287) / 3 = 861 / 3 ≈ 287
This solution is correct!
Solution 2:
287, 287, 287
Verification:
(287 + 287 + 287) / 3 = 861 / 3 ≈ 287
This solution is correct!
Solution 3:
131, 409, 321
Verification:
(131 + 409 + 321) / 3 = 861 / 3 ≈ 287
This solution is correct!
Solution 4:
619, 222, 20
Verification:
(619 + 222 + 20) / 3 = 861 / 3 ≈ 287
This solution is correct!
Solution 5:
30, 778, 53
Verification:
(30 + 778 + 53) / 3 = 861 / 3 ≈ 287
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 861 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.