What three numbers have an average of 116?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 116. This means if we add these three numbers together and divide by 3, we should get 116.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 116 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 116 * 3 = x + y + z
- So, the sum of our three numbers should be: 348
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 348.
Solution 1:
116, 116, 116
Verification:
(116 + 116 + 116) / 3 = 348 / 3 ≈ 116
This solution is correct!
Solution 2:
116, 116, 116
Verification:
(116 + 116 + 116) / 3 = 348 / 3 ≈ 116
This solution is correct!
Solution 3:
215, 86, 47
Verification:
(215 + 86 + 47) / 3 = 348 / 3 ≈ 116
This solution is correct!
Solution 4:
65, 137, 146
Verification:
(65 + 137 + 146) / 3 = 348 / 3 ≈ 116
This solution is correct!
Solution 5:
316, 7, 25
Verification:
(316 + 7 + 25) / 3 = 348 / 3 ≈ 116
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 348 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.