What three numbers have an average of 98?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 98. This means if we add these three numbers together and divide by 3, we should get 98.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 98 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 98 * 3 = x + y + z
- So, the sum of our three numbers should be: 294
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 294.
Solution 1:
98, 98, 98
Verification:
(98 + 98 + 98) / 3 = 294 / 3 ≈ 98
This solution is correct!
Solution 2:
98, 98, 98
Verification:
(98 + 98 + 98) / 3 = 294 / 3 ≈ 98
This solution is correct!
Solution 3:
233, 6, 55
Verification:
(233 + 6 + 55) / 3 = 294 / 3 ≈ 98
This solution is correct!
Solution 4:
227, 6, 61
Verification:
(227 + 6 + 61) / 3 = 294 / 3 ≈ 98
This solution is correct!
Solution 5:
188, 78, 28
Verification:
(188 + 78 + 28) / 3 = 294 / 3 ≈ 98
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 294 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.