What three numbers have an average of 136?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 136. This means if we add these three numbers together and divide by 3, we should get 136.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 136 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 136 * 3 = x + y + z
- So, the sum of our three numbers should be: 408
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 408.
Solution 1:
136, 136, 136
Verification:
(136 + 136 + 136) / 3 = 408 / 3 ≈ 136
This solution is correct!
Solution 2:
136, 136, 136
Verification:
(136 + 136 + 136) / 3 = 408 / 3 ≈ 136
This solution is correct!
Solution 3:
134, 171, 103
Verification:
(134 + 171 + 103) / 3 = 408 / 3 ≈ 136
This solution is correct!
Solution 4:
114, 139, 155
Verification:
(114 + 139 + 155) / 3 = 408 / 3 ≈ 136
This solution is correct!
Solution 5:
107, 296, 5
Verification:
(107 + 296 + 5) / 3 = 408 / 3 ≈ 136
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 408 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.