What three numbers have an average of 105?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 105. This means if we add these three numbers together and divide by 3, we should get 105.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 105 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 105 * 3 = x + y + z
- So, the sum of our three numbers should be: 315
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 315.
Solution 1:
105, 105, 105
Verification:
(105 + 105 + 105) / 3 = 315 / 3 ≈ 105
This solution is correct!
Solution 2:
105, 105, 105
Verification:
(105 + 105 + 105) / 3 = 315 / 3 ≈ 105
This solution is correct!
Solution 3:
130, 76, 109
Verification:
(130 + 76 + 109) / 3 = 315 / 3 ≈ 105
This solution is correct!
Solution 4:
16, 221, 78
Verification:
(16 + 221 + 78) / 3 = 315 / 3 ≈ 105
This solution is correct!
Solution 5:
287, 10, 18
Verification:
(287 + 10 + 18) / 3 = 315 / 3 ≈ 105
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 315 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.