What three numbers have an average of 34?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 34. This means if we add these three numbers together and divide by 3, we should get 34.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 34 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 34 * 3 = x + y + z
- So, the sum of our three numbers should be: 102
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 102.
Solution 1:
34, 34, 34
Verification:
(34 + 34 + 34) / 3 = 102 / 3 ≈ 34
This solution is correct!
Solution 2:
34, 34, 34
Verification:
(34 + 34 + 34) / 3 = 102 / 3 ≈ 34
This solution is correct!
Solution 3:
74, 1, 27
Verification:
(74 + 1 + 27) / 3 = 102 / 3 ≈ 34
This solution is correct!
Solution 4:
32, 4, 66
Verification:
(32 + 4 + 66) / 3 = 102 / 3 ≈ 34
This solution is correct!
Solution 5:
31, 66, 5
Verification:
(31 + 66 + 5) / 3 = 102 / 3 ≈ 34
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 102 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.