What three numbers have an average of 285?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 285. This means if we add these three numbers together and divide by 3, we should get 285.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 285 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 285 * 3 = x + y + z
- So, the sum of our three numbers should be: 855
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 855.
Solution 1:
285, 285, 285
Verification:
(285 + 285 + 285) / 3 = 855 / 3 ≈ 285
This solution is correct!
Solution 2:
285, 285, 285
Verification:
(285 + 285 + 285) / 3 = 855 / 3 ≈ 285
This solution is correct!
Solution 3:
417, 234, 204
Verification:
(417 + 234 + 204) / 3 = 855 / 3 ≈ 285
This solution is correct!
Solution 4:
171, 469, 215
Verification:
(171 + 469 + 215) / 3 = 855 / 3 ≈ 285
This solution is correct!
Solution 5:
474, 322, 59
Verification:
(474 + 322 + 59) / 3 = 855 / 3 ≈ 285
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 855 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.