What three numbers have an average of 96?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 96. This means if we add these three numbers together and divide by 3, we should get 96.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 96 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 96 * 3 = x + y + z
- So, the sum of our three numbers should be: 288
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 288.
Solution 1:
96, 96, 96
Verification:
(96 + 96 + 96) / 3 = 288 / 3 ≈ 96
This solution is correct!
Solution 2:
96, 96, 96
Verification:
(96 + 96 + 96) / 3 = 288 / 3 ≈ 96
This solution is correct!
Solution 3:
209, 45, 34
Verification:
(209 + 45 + 34) / 3 = 288 / 3 ≈ 96
This solution is correct!
Solution 4:
232, 6, 50
Verification:
(232 + 6 + 50) / 3 = 288 / 3 ≈ 96
This solution is correct!
Solution 5:
184, 35, 69
Verification:
(184 + 35 + 69) / 3 = 288 / 3 ≈ 96
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 288 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.