What three numbers have an average of 298?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 298. This means if we add these three numbers together and divide by 3, we should get 298.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 298 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 298 * 3 = x + y + z
- So, the sum of our three numbers should be: 894
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 894.
Solution 1:
298, 298, 298
Verification:
(298 + 298 + 298) / 3 = 894 / 3 ≈ 298
This solution is correct!
Solution 2:
298, 298, 298
Verification:
(298 + 298 + 298) / 3 = 894 / 3 ≈ 298
This solution is correct!
Solution 3:
871, 6, 17
Verification:
(871 + 6 + 17) / 3 = 894 / 3 ≈ 298
This solution is correct!
Solution 4:
306, 304, 284
Verification:
(306 + 304 + 284) / 3 = 894 / 3 ≈ 298
This solution is correct!
Solution 5:
374, 409, 111
Verification:
(374 + 409 + 111) / 3 = 894 / 3 ≈ 298
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 894 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.