What three numbers have an average of 294?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 294. This means if we add these three numbers together and divide by 3, we should get 294.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 294 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 294 * 3 = x + y + z
- So, the sum of our three numbers should be: 882
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 882.
Solution 1:
294, 294, 294
Verification:
(294 + 294 + 294) / 3 = 882 / 3 ≈ 294
This solution is correct!
Solution 2:
294, 294, 294
Verification:
(294 + 294 + 294) / 3 = 882 / 3 ≈ 294
This solution is correct!
Solution 3:
4, 327, 551
Verification:
(4 + 327 + 551) / 3 = 882 / 3 ≈ 294
This solution is correct!
Solution 4:
709, 24, 149
Verification:
(709 + 24 + 149) / 3 = 882 / 3 ≈ 294
This solution is correct!
Solution 5:
634, 61, 187
Verification:
(634 + 61 + 187) / 3 = 882 / 3 ≈ 294
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 882 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.