What three numbers have an average of 95?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 95. This means if we add these three numbers together and divide by 3, we should get 95.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 95 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 95 * 3 = x + y + z
- So, the sum of our three numbers should be: 285
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 285.
Solution 1:
95, 95, 95
Verification:
(95 + 95 + 95) / 3 = 285 / 3 ≈ 95
This solution is correct!
Solution 2:
95, 95, 95
Verification:
(95 + 95 + 95) / 3 = 285 / 3 ≈ 95
This solution is correct!
Solution 3:
198, 34, 53
Verification:
(198 + 34 + 53) / 3 = 285 / 3 ≈ 95
This solution is correct!
Solution 4:
98, 137, 50
Verification:
(98 + 137 + 50) / 3 = 285 / 3 ≈ 95
This solution is correct!
Solution 5:
171, 92, 22
Verification:
(171 + 92 + 22) / 3 = 285 / 3 ≈ 95
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 285 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.