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:
243, 131, 34
Verification:
(243 + 131 + 34) / 3 = 408 / 3 ≈ 136
This solution is correct!
Solution 4:
293, 76, 39
Verification:
(293 + 76 + 39) / 3 = 408 / 3 ≈ 136
This solution is correct!
Solution 5:
150, 187, 71
Verification:
(150 + 187 + 71) / 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.