What three numbers have an average of 109?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 109. This means if we add these three numbers together and divide by 3, we should get 109.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 109 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 109 * 3 = x + y + z
- So, the sum of our three numbers should be: 327
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 327.
Solution 1:
109, 109, 109
Verification:
(109 + 109 + 109) / 3 = 327 / 3 ≈ 109
This solution is correct!
Solution 2:
109, 109, 109
Verification:
(109 + 109 + 109) / 3 = 327 / 3 ≈ 109
This solution is correct!
Solution 3:
132, 17, 178
Verification:
(132 + 17 + 178) / 3 = 327 / 3 ≈ 109
This solution is correct!
Solution 4:
86, 162, 79
Verification:
(86 + 162 + 79) / 3 = 327 / 3 ≈ 109
This solution is correct!
Solution 5:
241, 70, 16
Verification:
(241 + 70 + 16) / 3 = 327 / 3 ≈ 109
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 327 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.