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:
104, 72, 112
Verification:
(104 + 72 + 112) / 3 = 288 / 3 ≈ 96
This solution is correct!
Solution 4:
259, 6, 23
Verification:
(259 + 6 + 23) / 3 = 288 / 3 ≈ 96
This solution is correct!
Solution 5:
24, 244, 20
Verification:
(24 + 244 + 20) / 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.