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:
736, 34, 112
Verification:
(736 + 34 + 112) / 3 = 882 / 3 ≈ 294
This solution is correct!
Solution 4:
660, 99, 123
Verification:
(660 + 99 + 123) / 3 = 882 / 3 ≈ 294
This solution is correct!
Solution 5:
41, 20, 821
Verification:
(41 + 20 + 821) / 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.