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:
185, 23, 86
Verification:
(185 + 23 + 86) / 3 = 294 / 3 ≈ 98
This solution is correct!
Solution 4:
127, 25, 142
Verification:
(127 + 25 + 142) / 3 = 294 / 3 ≈ 98
This solution is correct!
Solution 5:
80, 106, 108
Verification:
(80 + 106 + 108) / 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.